MAT147 – College Trigonometry

Course Overview

This course is designed for students majoring in mathematics, science, or engineering. It covers trigonometric functions, identities, equations, and applications, with a focus on graphical analysis and problem-solving. Students will learn to solve triangles, apply the Law of Sines and Law of Cosines, and use trigonometric identities in various contexts.

• Credits: 3 (Lecture Hours)

• Prerequisites: MAT-108 or equivalent

• Instructor: Sean Evans

• Semester: Fall 2025

• Location: Allegheny Campus, Milton Hall M305

Main Topics and Learning Outcomes

• Graph trigonometric functions

• Establish trigonometric identities

• Solve trigonometric equations

• Solve triangles using right triangle trigonometry

• Solve oblique triangles using the Law of Sines and Law of Cosines

Course Content and Structure

Trigonometric Functions

Trigonometric functions describe the relationships between the angles and sides of triangles, particularly right triangles. They are fundamental in analyzing periodic phenomena and solving geometric problems.

• Key Functions: Sine (), Cosine (), Tangent (), Cotangent (), Secant (), Cosecant ()

• Unit Circle: The unit circle is used to define trigonometric functions for all real numbers.

• Graphs: Each function has a distinct graph, characterized by amplitude, period, phase shift, and vertical shift.

• Example: The graph of has a period of and amplitude of 1.

Trigonometric Identities

Trigonometric identities are equations involving trigonometric functions that hold true for all values of the variables involved. They are essential for simplifying expressions and solving equations.

• Fundamental Identities:

• Angle Sum and Difference Identities:

• Double Angle Identities:

• Example: Simplify using the Pythagorean identity.

Solving Trigonometric Equations

Trigonometric equations involve unknown angles or values within trigonometric functions. Solving these equations often requires the use of identities and algebraic manipulation.

• General Solution: For , or , where is any integer.

• Example: Solve for in .

Right Triangle Trigonometry

Right triangle trigonometry focuses on the relationships between the angles and sides of right triangles. It is foundational for solving geometric problems and applications in physics and engineering.

• Definitions:

• Applications: Finding unknown sides or angles in right triangles.

• Example: Given a right triangle with hypotenuse 10 and angle , find the length of the side opposite .

Oblique Triangle Trigonometry

Oblique triangles are triangles without a right angle. The Law of Sines and Law of Cosines are used to solve for unknown sides and angles.

• Law of Sines:

• Law of Cosines:

• Applications: Solving for missing sides or angles in non-right triangles.

• Example: Given , , and , find using the Law of Cosines.

Course Policies and Procedures

Evaluation Plan

• Unit 1 Exam (15%)

• Unit 2 Exam (15%)

• Unit 3 Exam (15%)

• Unit 4 Exam (15%)

• Cumulative Final Exam (20%)

• MyMathLab (20%)

Grading Scale:

Attendance and Tardiness

• Attendance is checked during lectures.

• Students are responsible for obtaining missed notes and assignments.

Test and Quiz Policies

• Exams dates are TBA.

• Makeup exams require prior notification and approval.

• Quizzes are infrequent and may include bonus points.

• Calculators are generally not permitted for quizzes/exams; a basic trigonometric calculator may be required for later exams.

Homework

• Homework is completed via WebAssign and MyMathLab.

• MyMathLab access code and eBook are required.

• Assignments follow a regular schedule, typically due on Sundays.

Communication

• All official communication is via CCAC email.

• Announcements are posted on Blackboard.

• Students must regularly check their CCAC email for updates.

Academic Honesty

• Cheating is defined as misrepresentation of mastery on academic exercises.

• Academic dishonesty will result in disciplinary action.

General Education Goals

Required Materials

• Textbook: Precalculus by Sullivan (12th ed., Pearson, 2020)

• MyMathLab Access Code (Pearson platform)

• Calculator: Basic trigonometric calculator for later exams

Support Resources

• Math Café: Tutoring available in Library Building L313 and via ZOOM

• Blackboard: Used for distributing sample tests, organizing ZOOM meetings, and posting materials

Additional Info

• Course may move to ZOOM format if directed by the college.

• Students are expected to follow Student Handbook guidelines for online conduct.

• Partial credit may be awarded on exams if procedures are shown.