Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
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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
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Transcendental Functions
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Calculus III

Course: Trigonometry
Topic: Trigonometric Equations
Subtopic: Equations Involving Inverse Trig Function

Overview

Our goal in this lesson is to meld inverse trigonometric functions and trigonometric equations. When a trigonometric equation involves a single inverse trigonometric function, isolate it, and "undo" it by applying the corresponding regular trig function to both sides of the equation which will isolate the variable input. For example, 2sin^-1x=pi rArr arcsinx=pi/2 rArr sin(arcsinx)=sin(pi/2) rArr x=sin(pi/2)=1.

Objectives

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

• 6.4.1 Algebraically solve trigonometric equations that involve a single inverse trig function
• 6.4.2 Graphically solve trigonometric equations that involve a single inverse trig function
• 6.4.4 Electronically solve trigonometric equations that involve a single inverse trig function
• 6.4.5 Recognize when a trigonometric equation that involves an inverse trig function has no solution

Text Notes

Most textbooks go beyond equations that contain a single inverse trigonometric function to equations that contain multiple inverse trigonometric functions. These require a trig identity be applied, which can get particularly tricky. You can SKIP this type of equation. You will not be tested on equations that contain more than one inverse trigonometric function.

Mini-Lectures and Examples

rev. 2020-10-31