# Trigonometry

### Trigonometry Syllabus

• Course Code: Math 210

Transcript:

Yes. Your transcript will come from the records office at United States University. They are regionally accredited and award semester credits.

Credits: 3 Semester

Transfer: 4 year degree applicable

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

No outside textbook is needed. Our Omega MathTM courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest example, and then moves slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.

Proctored Final: Yes

#### Description

This course provides a study of the relationships between angles and sides of triangles, relationships between central angles and coordinate points on a circle, right triangles, circular functions, degree/radian measures of angles, trigonometric functions of angles, inverse functions, identities, graphic representations of trigonometric functions, law of sines and cosines, trigonometric equations, solutions of right and oblique triangles, vectors, complex numbers, and polar coordinates. Upon completion, students will be able to solve practical problems and use appropriate models for analysis.
Prerequisite: Intermediate Algebra with a grade of C or better. Precalculus or College Algebra with a grade of C or better is recommended.
UC Approved: Yes
Meets Common Core Requirements: Yes

#### Learning Outcomes

At the conclusion of this course, students should have:

1. Describe the fundamental principles including the laws and theorems which come from the concepts of trigonometry.
2. Solve problems using the Pythagorean Theorem and the distance formula.
3. Use trigonometric terminology, notation and symbols.
4. Transfer degrees to radian measure and vice versa.
5. Demonstrate an understanding of the six trigonometric functions.
6. Analyze and interpret trigonometric functions using graphs, tables and equations.
7. Define signs of trigonometric functions for each quadrant.
8. Solve problems involving special right triangles using exact ratios.
9. Solve problems involving oblique and right triangles.
10. Solve trigonometric equations.
11. Graph trigonometric functions, and their inverses.
12. Verify and apply trigonometric identities.
13. Solve problems using inverse trigonometric functions.
14. Solve problems involving Law of Sines and Law of Cosines.
15. Model situations from a variety of settings using trigonometric functions. Apply a variety of problem-solving strategies, including algebraic, numerical, and graphical techniques, to solve multiple-step problems involving trigonometric equations and identities.
16. Demonstrate an understanding of vectors, their graphical representation and vector algebra.
17. Solve trigonometric problems involving complex numbers.
18. Sketch and identify graphs using parametric equations. Convert rectangular equations to parametric form and vice versa.
19. Sketch and identify graphs using polar equations. Convert rectangular equations to polar form and vice versa.
20. Demonstrate real-world problem solving skills. Analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

#### Methods of Evaluation:

Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Proctored Final: 25%

This course go towards a degree which means it must have a proctored final. Your college is accepting this course because it goes through a regionally accredited university, which tells them the class will have a proctored final, and the 60% rule will apply. Your college will not accept a class from a school that is not regionally accredited, because they know these standards won't be met.

The final exam must be proctored at college testing center or a Sylvan Learning Center. A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near your home: Proctored Final

The final exam is a comprehensive final covering all of the chapters of the course. Other than scratch paper, you may view the "Authorized Materials" list for the final exam for each class.

• Students must obtain a 60% or better on the final exam in order to get a C or better in the class.
• Students that obtain a grade of an F on the final can receive at most a D in the class. Students that obtain a D on the final can receive at most a C in the class. Students that obtain a C on the final can receive at most a B in the class.

The 60% rule was set in place to protect the integrity of online math education by requiring a display of competency in exchange for a grade. All schools which are regionally accredited adhere to online standards. Your college is accepting this course because it goes through a regionally accredited university, which tells your college that standards have been met. Your college will not accept a class from a school that is not regionally accredited, because they know the standards won't be met.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Instructional Process: In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.

## Chapter 1

The Six Trigonometric Functions

Lessons Homework HW Quiz
1.1   The Rectangular Coordinate System 1.1 1.1
1.2   Angles, Degrees and Special Triangles 1.2 1.2
1.3   Trigonometric Functions 1.3 1.3
1.4   Introduction to the Unit Circle 1.4 1.4
Chapter 1 Test   (25 questions)

## Chapter 2

Trigonometry

Lessons Homework HW Quiz
2.1   Right Triangle Trigonometry 2.1 2.1
2.2   Other Angles and Trigonometric Functions 2.2 2.2
2.3   Solving Right Triangles 2.3 2.3
2.4   Applications 2.4 2.4
Chapter 2 Test   (18 questions)

## Chapter 3

Lessons Homework HW Quiz
3.1   Reference Angle 3.1 3.1
3.2   Radians and Degrees 3.2 3.2
3.3   Circular Functions 3.3 3.3
3.4   Arc Length and Area of a Sector 3.4 3.4
3.5   Velocity 3.5 3.5
Chapter 3 Test   (22 questions)

## Chapter 4

Graphs of Trigonometric Functions

Lessons Homework HW Quiz
4.1   Graphs of Basic Trigonometric Functions 4.1 4.1
4.2   Amplitude and Period 4.2 4.2
4.3   Phase Shift 4.3 4.3
4.4   Equations of Graphs 4.4 4.4
4.5   Relations and Functions 4.5 4.5
4.6   Inverse Trigonometric Functions 4.6 4.6
Chapter 4 Test   (23 questions)

## Chapter 5

Trigonometric Identities

Lessons Homework HW Quiz
5.1   Proving Identities 5.1 5.1
5.2   Sum and Difference Formula 5.2 5.2
5.3   Double-Angle Formula 5.3 5.3
5.4   Half-Angle Formula 5.4 5.4
5.5   More Identities 5.5 5.5
Chapter 5 Test   (22 questions)

## Chapter 6

Trigonometric Equations

Lessons Homework HW Quiz
6.1   Trigonometric Equations 6.1 6.1
6.2   More Trigonometric Equations 6.2 6.2
6.3   Trigonometric Equations & Multiple Angles 6.3 6.3
6.4   Parametric Equations 6.4 6.4
Chapter 6 Test   (21 questions)

## Chapter 7

Triangles

Lessons Homework HW Quiz
7.1   Law of Cosines 7.1 7.1
7.2   Law of Sines 7.2 7.2
7.3   Area of a Triangle 7.3 7.3
7.4   Vectors 7.4 7.4
Chapter 7 Test   (22 questions)

## Chapter 8

Polar Coordinates & Complex Numbers

Lessons Homework HW Quiz
8.1   Complex Numbers 8.1 8.1
8.2   Trigonometric Form of a Complex Number 8.2 8.2
8.3   Products and Quotients in Trigonometric Form 8.3 8.3
8.4   Roots of a Complex Number 8.4 8.4
8.5   Polar Coordinates 8.5 8.5
8.6   Equations of Polar Coordinates and their Graphs 8.6 8.6
Chapter 8 Test   (21 questions)
 Final for Trigonometry   (54 questions)

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 1.1 - 1.3 2 1.4 - 2.2 3 2.3 - 3.1 4 3.2 - 3.3 5 3.4 - 3.5 6 4.1 - 4.2 7 4.3 - 4.4 8 45 - 4.6 9 5.1 - 5.2 10 5.3 - 5.4 11 5.5 - 6.1 12 6.2 - 6.3 13 6.4 - 7.1 14 7.2 - 7.4 15 8.1 - 8.3 16 8.4 - 8.6 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Grading information and proctored final policies:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.

• Course Code: MATU 8000

Transcript:

Yes. Your transcript will come from the records office at Brandman University. They are regionally accredited and award Proffessional Development Units (PDU).

Credits: 3 Professional Development Units (PDU)

Transfer:

Since Professional Development units (PDU) are not academic credits, they typically cannot be used towards graduation of an undergraduate degree. However, the course may be able to be used as a prerequisite at some schools and/or graduate programs. Since graduate programs usually just need to verify the course has been taken, PDUs are usually acceptable. Ask your counselor for pre-approval by sending him/her the Course Description on Brandman's Site. The course can also be used to learn the material and then receive credit at your college using Credit by Examination. (K-12 use)

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

No outside textbook is needed. Our Omega MathTM courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest example, and then moves slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.

Proctored Final: No

#### Description

This course provides a study of the relationships between angles and sides of triangles, relationships between central angles and coordinate points on a circle, right triangles, circular functions, degree/radian measures of angles, trigonometric functions of angles, inverse functions, identities, graphic representations of trigonometric functions, law of sines and cosines, trigonometric equations, solutions of right and oblique triangles equations, vectors, complex numbers, and polar coordinates. Upon completion, students should be able to solve practical problems and use appropriate models for analysis.
Prerequisite: Intermediate Algebra with a grade of C or better. Precalculus or College Algebra with a grade of C or better is recommended.
UC Approved: Yes
Meets Common Core Requirements: Yes

#### Learning Outcomes

At the conclusion of this course, students should have:

1. Describe the fundamental principles including the laws and theorems which come from the concepts of Trigonometry.
2. Solve problems using the Pythagorean Theorem and distance formula.
3. Use trigonometric terminology, notation and symbols.
4. Transfer degrees to radian measure and vice versa.
5. Demonstrate an understanding of the trigonometric functions.
6. Analyze and interpret trigonometric functions using graphs, tables and equations.
7. Define signs of trigonometric functions for each quadrant.
8. Solve problems involving special right triangles using exact ratios.
9. Use a graphing calculator for trigonometric computations as well as other values such as minimum and/or maximum of functions.
10. Solve problems involving oblique and right triangles.
11. Solve problems involving radian measures.
12. Solve trigonometric equations.
13. Graph trigonometric functions.
14. Verify and apply trigonometric identities.
15. Solve problems using the inverse trigonometric functions.
16. Solve problems involving Law of Sines and Law of Cosines.
17. Model situations from a variety of settings using trigonometric functions. Apply a variety of problem-solving strategies, including algebraic, numerical, and graphical techniques, to solve multiple-step problems involving trigonometric equations and identities.
18. Demonstrate an understanding of vectors, their graphical representation and vector algebra.
19. Solve trigonometric problems involving complex numbers.
20. Sketch and identify graphs using parametric equations. Convert rectangular equations to parametric form and vice versa.
21. Sketch and identify graphs using polar equations. Convert rectangular equations to polar form and vice versa.
22. Demonstrate real-world problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

#### Methods of Evaluation:

Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Instructional Process: In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.

## Chapter 1

The Six Trigonometric Functions

Lessons Homework HW Quiz
1.1   The Rectangular Coordinate System 1.1 1.1
1.2   Angles, Degrees and Special Triangles 1.2 1.2
1.3   Trigonometric Functions 1.3 1.3
1.4   Introduction to the Unit Circle 1.4 1.4
Chapter 1 Test   (25 questions)

## Chapter 2

Trigonometry

Lessons Homework HW Quiz
2.1   Right Triangle Trigonometry 2.1 2.1
2.2   Other Angles and Trigonometric Functions 2.2 2.2
2.3   Solving Right Triangles 2.3 2.3
2.4   Applications 2.4 2.4
Chapter 2 Test   (18 questions)

## Chapter 3

Lessons Homework HW Quiz
3.1   Reference Angle 3.1 3.1
3.2   Radians and Degrees 3.2 3.2
3.3   Circular Functions 3.3 3.3
3.4   Arc Length and Area of a Sector 3.4 3.4
3.5   Velocity 3.5 3.5
Chapter 3 Test   (22 questions)

## Chapter 4

Graphs of Trigonometric Functions

Lessons Homework HW Quiz
4.1   Graphs of Basic Trigonometric Functions 4.1 4.1
4.2   Amplitude and Period 4.2 4.2
4.3   Phase Shift 4.3 4.3
4.4   Equations of Graphs 4.4 4.4
4.5   Relations and Functions 4.5 4.5
4.6   Inverse Trigonometric Functions 4.6 4.6
Chapter 4 Test   (23 questions)

## Chapter 5

Trigonometric Identities

Lessons Homework HW Quiz
5.1   Proving Identities 5.1 5.1
5.2   Sum and Difference Formula 5.2 5.2
5.3   Double-Angle Formula 5.3 5.3
5.4   Half-Angle Formula 5.4 5.4
5.5   More Identities 5.5 5.5
Chapter 5 Test   (22 questions)

## Chapter 6

Trigonometric Equations

Lessons Homework HW Quiz
6.1   Trigonometric Equations 6.1 6.1
6.2   More Trigonometric Equations 6.2 6.2
6.3   Trigonometric Equations & Multiple Angles 6.3 6.3
6.4   Parametric Equations 6.4 6.4
Chapter 6 Test   (21 questions)

## Chapter 7

Triangles

Lessons Homework HW Quiz
7.1   Law of Cosines 7.1 7.1
7.2   Law of Sines 7.2 7.2
7.3   Area of a Triangle 7.3 7.3
7.4   Vectors 7.4 7.4
Chapter 7 Test   (22 questions)

## Chapter 8

Polar Coordinates & Complex Numbers

Lessons Homework HW Quiz
8.1   Complex Numbers 8.1 8.1
8.2   Trigonometric Form of a Complex Number 8.2 8.2
8.3   Products and Quotients in Trigonometric Form 8.3 8.3
8.4   Roots of a Complex Number 8.4 8.4
8.5   Polar Coordinates 8.5 8.5
8.6   Equations of Polar Coordinates and their Graphs 8.6 8.6
Chapter 8 Test   (21 questions)
 Final for Trigonometry   (53 questions)

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 1.1 - 1.3 2 1.4 - 2.2 3 2.3 - 3.1 4 3.2 - 3.3 5 3.4 - 3.5 6 4.1 - 4.2 7 4.3 - 4.4 8 45 - 4.6 9 5.1 - 5.2 10 5.3 - 5.4 11 5.5 - 6.1 12 6.2 - 6.3 13 6.4 - 7.1 14 7.2 - 7.3 15 7.4 - 8.1 16 8.2 - 8.3 17 8.4 - 8.6 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Grading information and proctored final policies:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.

• Course Code: None

Transcript:

A certificate of completion is issued from Omega Math. This course under the non-credit option does not go through one of our partner universities; thus, a transcript is not included with the course.

Credits: 0

Certificate of Completion: Yes

Transfer:

Some of our Associated Schools permit their students to take this course under the non-credit option, and use it as a prerequisite for the next course. Check the list to see if your college permits this non-credit option. If your school is not on this list and you want to transfer the course to your college, you will need to enroll under the semester credit option. If you would like pre-approval from your school, please send your counselor or registrar's office the link to this page. If you would like to take this class for personal enrichment, the non-credit course is the exact same class as the credit course; it is just less expensive since it is not sent through our partner university for credit. The non-credit courses can also be used to learn the material and then receive credit at a home college using Credit by Examination.
(K-12 use)

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

No outside textbook is needed. Our Omega MathTM courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest example, and then moves slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.

Proctored Final: No

#### Description

This course provides a study of the relationships between angles and sides of triangles, relationships between central angles and coordinate points on a circle, right triangles, circular functions, degree/radian measures of angles, trigonometric functions of angles, inverse functions, identities, graphic representations of trigonometric functions, law of sines and cosines, trigonometric equations, solutions of right and oblique triangles equations, vectors, complex numbers, and polar coordinates. Upon completion, students should be able to solve practical problems and use appropriate models for analysis. This course is designed to prepare students for further study in mathematics required in the sciences and other technical fields.
Prerequisite: Intermediate Algebra with a grade of C or better. Precalculus or College Algebra with a grade of C or better is recommended.
UC Approved: Yes
Meets Common Core Requirements: Yes

#### Learning Outcomes

At the conclusion of this course, students should have:

1. Describe the fundamental principles including the laws and theorems which come from the concepts of Trigonometry.
2. Solve problems using the Pythagorean Theorem and distance formula.
3. Use trigonometric terminology, notation and symbols.
4. Transfer degrees to radian measure and vice versa.
5. Demonstrate an understanding of the trigonometric functions.
6. Analyze and interpret trigonometric functions using graphs, tables and equations.
7. Define signs of trigonometric functions for each quadrant.
8. Solve problems involving special right triangles using exact ratios.
9. Use a graphing calculator for trigonometric computations as well as other values such as minimum and/or maximum of functions.
10. Solve problems involving oblique and right triangles.
11. Solve problems involving radian measures.
12. Solve trigonometric equations.
13. Graph trigonometric functions.
14. Verify and apply trigonometric identities.
15. Solve problems using the inverse trigonometric functions.
16. Solve problems involving Law of Sines and Law of Cosines.
17. Model situations from a variety of settings using trigonometric functions. Apply a variety of problem-solving strategies, including algebraic, numerical, and graphical techniques, to solve multiple-step problems involving trigonometric equations and identities.
18. Demonstrate an understanding of vectors, their graphical representation and vector algebra.
19. Solve trigonometric problems involving complex numbers.
20. Sketch and identify graphs using parametric equations. Convert rectangular equations to parametric form and vice versa.
21. Sketch and identify graphs using polar equations. Convert rectangular equations to polar form and vice versa.
22. Demonstrate real-world problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

#### Methods of Evaluation:

Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Instructional Process: In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.

## Chapter 1

The Six Trigonometric Functions

Lessons Homework HW Quiz
1.1   The Rectangular Coordinate System 1.1 1.1
1.2   Angles, Degrees and Special Triangles 1.2 1.2
1.3   Trigonometric Functions 1.3 1.3
1.4   Introduction to the Unit Circle 1.4 1.4
Chapter 1 Test   (25 questions)

## Chapter 2

Trigonometry

Lessons Homework HW Quiz
2.1   Right Triangle Trigonometry 2.1 2.1
2.2   Other Angles and Trigonometric Functions 2.2 2.2
2.3   Solving Right Triangles 2.3 2.3
2.4   Applications 2.4 2.4
Chapter 2 Test   (18 questions)

## Chapter 3

Lessons Homework HW Quiz
3.1   Reference Angle 3.1 3.1
3.2   Radians and Degrees 3.2 3.2
3.3   Circular Functions 3.3 3.3
3.4   Arc Length and Area of a Sector 3.4 3.4
3.5   Velocity 3.5 3.5
Chapter 3 Test   (22 questions)

## Chapter 4

Graphs of Trigonometric Functions

Lessons Homework HW Quiz
4.1   Graphs of Basic Trigonometric Functions 4.1 4.1
4.2   Amplitude and Period 4.2 4.2
4.3   Phase Shift 4.3 4.3
4.4   Equations of Graphs 4.4 4.4
4.5   Relations and Functions 4.5 4.5
4.6   Inverse Trigonometric Functions 4.6 4.6
Chapter 4 Test   (23 questions)

## Chapter 5

Trigonometric Identities

Lessons Homework HW Quiz
5.1   Proving Identities 5.1 5.1
5.2   Sum and Difference Formula 5.2 5.2
5.3   Double-Angle Formula 5.3 5.3
5.4   Half-Angle Formula 5.4 5.4
5.5   More Identities 5.5 5.5
Chapter 5 Test   (22 questions)

## Chapter 6

Trigonometric Equations

Lessons Homework HW Quiz
6.1   Trigonometric Equations 6.1 6.1
6.2   More Trigonometric Equations 6.2 6.2
6.3   Trigonometric Equations & Multiple Angles 6.3 6.3
6.4   Parametric Equations 6.4 6.4
Chapter 6 Test   (21 questions)

## Chapter 7

Triangles

Lessons Homework HW Quiz
7.1   Law of Cosines 7.1 7.1
7.2   Law of Sines 7.2 7.2
7.3   Area of a Triangle 7.3 7.3
7.4   Vectors 7.4 7.4
Chapter 7 Test   (22 questions)

## Chapter 8

Polar Coordinates & Complex Numbers

Lessons Homework HW Quiz
8.1   Complex Numbers 8.1 8.1
8.2   Trigonometric Form of a Complex Number 8.2 8.2
8.3   Products and Quotients in Trigonometric Form 8.3 8.3
8.4   Roots of a Complex Number 8.4 8.4
8.5   Polar Coordinates 8.5 8.5
8.6   Equations of Polar Coordinates and their Graphs 8.6 8.6
Chapter 8 Test   (21 questions)
 Final for Trigonometry   (53 questions)

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 1.1 - 1.3 2 1.4 - 2.2 3 2.3 - 3.1 4 3.2 - 3.3 5 3.4 - 4.1 6 4.2 - 4.3 7 4.4 - 4.6 8 5.1 - 5.2 9 5.3 - 5.5 10 6.1 - 6.2 11 6.3 - 7.1 12 7.2 - 7.3 13 7.4 - 8.1 14 8.2 - 8.3 15 8.4 - 8.5 16 8.6 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Grading information and proctored final policies:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.