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 Identities
Subtopic: Identities Involving Inverse Trig Functions

Overview

Our goal in this lesson is to meld inverse trigonometric functions and trigonometric identities. Here we simplify expressions that contain inverse trig functions and in some way involve a trig identity too. This topic involves taking quite complicated expressions (such as cos(arcsin(0.6) - arctan(-2)) and sin(2 cos^-1(x/sqrt2))) and simplifying algebraically via circle diagrams and trigonometric identities.

Objectives

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

• 5.5.1 Algebraically simplify expressions (both numeric and algebraic) that contain inverse trig functions and, in order to simplify, require the use of trig identities such as double-angle or sum/difference identities along with circle diagrams (perhaps even multiple circle diagrams)

Mini-Lectures and Examples

rev. 2020-10-19