MA 108 - Trigonometry

Description
Math 108 is designed to prepare students for higher level mathematics courses, especially for those who plan on taking calculus. Topics include angular measure, development of trigonometric functions, trigonometric identitites, reductions, radian measure, variation and graphs of trigonometric functions, functions of composite angles, identities including composite angles, right triangles and applications, oblique triangles and applications, trigonometric equations, and inverse trigonometric functions.

Credit Hours: 3
Contact Hours: 3

School: School of STEM
Department: Mathematics
Discipline: MA

Major Course Revisions: General Education Review
Last Revision Date Effective: 20220213T19:33:15
Course Review & Revision Year: 2026-2027

Course Type:
General Education- Offering designed to meet the specific criteria for a GRCC Distribution Requirement. The course should be designated by the requirement it fulfills.
Course Format:
Lecture - 1:1

General Education Requirement: Mathematics
General Education Learner Outcomes (GELO):
3. Critical Thinking: Gather and synthesize relevant information, evaluate alternative perspectives, or understand inquiry as a means of creating knowledge, 7. Problem-Solving: Apply theory, calculation, or experimentation to demonstrate effective problem-solving

Course Learning Outcomes:
1. Convert between radian and degree measure.

2. Find the other five trigonometric functions values given one trigonometric function value.

3. Derive the trigonometric values of 0, 30, 45, 60, and 90 degrees and their multiples.

4. Be able to use the eight fundamental trigonometric identities to solve problems and prove other identities.

5. Sketch the graphs of equations involving all six trigonometric functions.

6. Determine the domain, range, period, and amplitude of all six trigonometric functions.

7. Apply trigonometric skills to solve real world right triangles and problems using the trigonometric functions. (GELO 7)

8. Solve oblique triangle problems by use of the law of sines and the law of cosines.

9. Apply algebraic techniques in order to solve a trigonometric equation.

10. Find the value of an inverse function and graph inverse functions.

11. Identify the best solution to a problem. (GELO 3)

Approved for Online Delivery?: Yes

Course Outline:
I. Angle and arc measure

A. Degree

B. Radian

C. Arc length

II. Trigonometric Definition

A. Right Triangles

1. Similar triangles

2. 30, 60, 90 and 45, 45, 90 triangles

3. Trigonometric ratios

4. Solving right triangles

5. Inverse trigonometric values

B. Rectangular Coordinate System/Unit Circle

1. Trigonometric functions with acute angles

2. Reference angles

3. Trigonometric functions for any angle in a coordinate system.

4. Exact values of special angles

5. Trigonometric values on a unit circle

6. Trigonometric values for quadrantal angles

7. Inverse trigonometric values

III. Graphing Trigonometric Functions

A. Graph variations of y=A+Bsin[C(x+D)] and y= A+Bcos[C(x+D)] and relate to tranformations of graphs

B. Identify the amplitude, period, phase shift, and vertical shift of graphs.

C. Model periodic applications using trigonometric function.

D. Graphs of Other Trigonometric Functions

1. Tangent and cotangent functions

2. Secant and cosecant functions

V. Identities

A. Fundamental Identities and Their Use

B. Verifying Trigonometric Identities

C. Sum, Difference and Cofunction Identities

D. Double-Angle and Half-Angle Identities

E. Product/Sum Identities

V. Inverse Trigonometric Function/Trigonometric Equations

A. Inverse sine, cosine, and tangent functions

B. Trigonometric Equations

1. Solving trigonometric Equations over one period

2. Solving trigonometric Equations for all x

VI. Additional Topics

A. Law of Sines

1. Derivation of the law of sines

2. Ambiguous case (SSA)

B. Law of cosines

C. Vectors

1. Addition of geometric vectors

2. Resolution of a vector into components

D. Polar Coordinates

1. Definition of polar coordinates

2. Conversion between polar and rectangular coordinates

3. Plotting points on a polar coordinate system

4. Graphing polar Equations (optional)

Mandatory CLO Competency Assessment Measures:
None

Name of Industry Recognize Credentials: None

Instructional Strategies:
Lecture: 0-80%
Facilitated Discussion: 10-60%
Collaborative Learning: 0-60%
Student Presentation: 0-5%

Mandatory Course Components:
None

Academic Program Prerequisite: None
Prerequisites/Other Requirements: MA 107 (C or Higher) or ALEKS score of 46 or Higher
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corerequisite(s): None
Course-Specific Placement Test: None
Course Aligned with IRW: NA
Consent to Enroll in Course: No Department Consent Required

Total Lecture Hours Per Week: 3
Faculty Credential Requirements:
18 graduate credit hours in discipline being taught (HLC Requirement), Master’s Degree (GRCC general requirement)
Faculty Credential Requirement Details: Standard hiring requirements for the Mathematics Department apply.

General Room Request: None

Maximum Course Enrollment: 33
Equivalent Courses: None
Dual Enrollment Allowed?: Yes
Accepted GRCC Advanced Placement (AP) Exam Credit: None
AP Min. Score: None
Number of Times Course can be taken for credit: 1
Programs Where This Courses is a Requirement:
Architectural Technology, A.A.A.S., Architectural Technology, A.A.A.S (Ferris State University-Facility Management), Plastics-Polymer Engineering Technology, A.A.A.S., Tooling and Manufacturing Technology, A.A.A.S., Tooling and Manufacturing Technology Certificate
Course Fees: $19.00
People Soft Course ID Number: 101070
Course CIP Code: 27.01

High School Articulation Agreements exist?: No
If yes, with which high schools?: NA
Non-Credit GRCC Agreement exist?: No
If yes, with which Departments?: NA
Corporate Articulation Agreement exist?: No
If yes, with which Companies?: NA