Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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

Overview

Continuing 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.

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

Terms you should be able to define: multiple angle (in a trig expression)

Mini-Lectures and Examples

Supplemental Resources (optional)

rev. 2020-10-31