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Course: Trigonometry
Topic: Trigonometric Equations
Subtopic: Equations with Multiple Angles

Overview

Concluding our study of solving trigonometric equations, today we look specifically at those with "messy" angles. The angles may be multiple angles (i.e., double-angles 2θ, triple-angles 3θ, quadruple angles, 4θ, etc.). Or the angles may involve a phase shift. These equations require that you be particularly careful to obtain all the answers that are possible within the given interval. We will also solve equations for every possible solution (i.e. all the coterminal answers) rather than restricting the solutions to a particular range. This is a tricky section!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 6.3.1 Algebraically solve trigonometric equations that involve a multiple angle
• 6.3.2 Algebraically solve trigonometric equations that involve a phase-shifted angle
• 6.3.3 Algebraically solve trigonometric equations whose angles are not restricted to a particular interval
• 6.3.4 Represent, in either radians or degrees, "all" coterminal angle solutions to a trigonometric equation

Terminology

Define: multiple angle (in a trig expression)

Supplemental Resources (optional)