# Trigonometry

**I. Course Prefix/Number: **
MAT 122

** Course Name: **
Trigonometry

** Credits: **
3 (3 lecture; 0 lab)

**II. Prerequisite **

MAT 110 with a minimum grade of C or appropriate score on the Mathematics Assessment Test; and MAT 080 or geometry proficiency.

**III. Course (Catalog) Description **

This course presents the applied and analytic aspects of trigonometry, radian measure, trigonometric functions and their inverses, identities, graphs, equations, triangles, vectors with applications and complex numbers.

**IV. Learning Objectives **

1. Classify, analyze and evaluate relations and functions.

2. Use the definition of radian measure to calculate arc length, radius, and angles on circles.

3. Measure angles, and calculate coterminal and reference angles, in both degrees and radians.

4. Calculate by hand, and using a calculator, the six basic trigonometric functions of angles, both in right triangles and on the unit circle.

5. Use basic trigonometric functions and their inverses to solve applications involving right triangles.

6. Graph basic trigonometric and inverse trigonometric functions.

7. Solve trigonometric equations, and prove and apply trigonometric identities.

8. Use sum and product of angle formulas and the laws of sines and cosines to solve applications involving triangles.

9. Cacluate sums and multiples of vectors, projections onto other vectors, dot products, and angles between vectors.

10. Graph and analyze parametric equations.

11. Graph and analyze polar equations.

12. Use technology to graph trigonometric functions and inverses, and to solve equations involving them.

2. Use the definition of radian measure to calculate arc length, radius, and angles on circles.

3. Measure angles, and calculate coterminal and reference angles, in both degrees and radians.

4. Calculate by hand, and using a calculator, the six basic trigonometric functions of angles, both in right triangles and on the unit circle.

5. Use basic trigonometric functions and their inverses to solve applications involving right triangles.

6. Graph basic trigonometric and inverse trigonometric functions.

7. Solve trigonometric equations, and prove and apply trigonometric identities.

8. Use sum and product of angle formulas and the laws of sines and cosines to solve applications involving triangles.

9. Cacluate sums and multiples of vectors, projections onto other vectors, dot products, and angles between vectors.

10. Graph and analyze parametric equations.

11. Graph and analyze polar equations.

12. Use technology to graph trigonometric functions and inverses, and to solve equations involving them.

**V. Academic Integrity **

Students and employees at Oakton Community College are required to demonstrate academic integrity
and follow Oakton's Code of Academic Conduct. This code prohibits:

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

**VI. Sequence of Topics **

A. Trigonometric Functions

1. Measurement of angles

2. Definition of Trigonometric Functions

a) Right triangle definition

b) Circular definition

3. Graphs of sine and cosine functions

4. Graphs of the other trigonometric functions and their graphs

5. Inverse trigonometric functions and their graphs

6. Trigonometric Identities

A. Pythagorean Identities

B. Sum and Difference Formulas

C. Multiple and Half Angle Formulas

D. Sum to Product; Product to Sum

7. Solving trigonometric equations

8. Applications

A. Complex numbers and their trigonometric form

B. Solving right triangles

C. Law of Sines; Law of Cosines

D. Roots and powers of complex numbers

E. Polar coordinates

F. Parametric equations

B. Vectors and Dot Products

1. Geometric and algebraic representation

2. Basic operations with vectors

3. Applications

C. Technology

1. Generate the complete graph of each trigonometric and inverse trigonometric function, including setting a proper window, tracing and zooming.

2. Graphically locate the x-intercepts, the relative extrema and determine asymptotic behaviors.

3. Graphically, numerically and/or symbolically solve equations.

1. Measurement of angles

2. Definition of Trigonometric Functions

a) Right triangle definition

b) Circular definition

3. Graphs of sine and cosine functions

4. Graphs of the other trigonometric functions and their graphs

5. Inverse trigonometric functions and their graphs

6. Trigonometric Identities

A. Pythagorean Identities

B. Sum and Difference Formulas

C. Multiple and Half Angle Formulas

D. Sum to Product; Product to Sum

7. Solving trigonometric equations

8. Applications

A. Complex numbers and their trigonometric form

B. Solving right triangles

C. Law of Sines; Law of Cosines

D. Roots and powers of complex numbers

E. Polar coordinates

F. Parametric equations

B. Vectors and Dot Products

1. Geometric and algebraic representation

2. Basic operations with vectors

3. Applications

C. Technology

1. Generate the complete graph of each trigonometric and inverse trigonometric function, including setting a proper window, tracing and zooming.

2. Graphically locate the x-intercepts, the relative extrema and determine asymptotic behaviors.

3. Graphically, numerically and/or symbolically solve equations.

**VII. Methods of Instruction **

(To be completed by instructor)

Methods of presentation can include lectures, discussion, demonstration, experimentation, audiovisual aids, group work, and regularly assigned homework. Calculators / computers will be used when appropriate.

Course may be taught as face-to-face, media-based, hybrid or online course.

Methods of presentation can include lectures, discussion, demonstration, experimentation, audiovisual aids, group work, and regularly assigned homework. Calculators / computers will be used when appropriate.

Course may be taught as face-to-face, media-based, hybrid or online course.

**VIII. Course Practices Required **

(To be completed by instructor)

**IX. Instructional Materials **

**Note:**Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".

Textbooks can also be found at our Mathematics Textbooks page.

**X. Methods of Evaluating Student Progress **

(To be completed by instructor)

Evaluation methods can include assignments, quizzes, chapter or major tests, individual or group projects, computer assignments and/or a final examination.

Evaluation methods can include assignments, quizzes, chapter or major tests, individual or group projects, computer assignments and/or a final examination.

**XI. Other Course Information **

Individual instructors will establish and announce specific policies regarding attendance, due dates and make-up work, incomplete grades, etc.

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.