Topic: Graphs of Trigonometric Functions
Subtopic: Inverse Trigonometric Functions
Overview
We have worked with inverse trig functions (such as tan-1(1/√3)=π/6) before, but primarily just evaluating them on a calculator or via the unit circle. In this lesson we formally define inverse trig functions and extend our knowledge about them including their exploring their graphs, domains, and ranges.
Before studying inverse trigonometric functions, I strongly recommend that you review inverse functions in general. See the supplementary resources below for review sites.
It is very important to remember that while regular functions take an angle input and output a ratio, inverse trig functions take a ratio input and output the corresponding angle. The answer from an inverse trig function is an angle. Note the units (degrees or radians) in which the output angle needs to be.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 4.6.1 Graph the three main inverse trig functions arcsin(x), arccos(x), arctan(x)
- 4.6.2 Know the domain and range of all six inverse trig functions
- 4.6.3 Know in which quadrants the answers from each of the six inverse trig functions lie (important!)
- 4.6.4 Evaluate inverse trig functions manually
- 4.6.5 Evaluate compositions of trig and inverse trig functions both numeric, such as tan(cos-1(-√3/2)), and algebraic, such as sec(sin-1(x))
Terminology
Define: vertical and horizontal line tests, one-to-one trig function, inverse trigonometric function
Supplementary Resources
Need a general review of inverse functions? The Math Page's Topics in Precalculus: Inverse Functions provides an overall review of inverse functions. PurpleMath's Inverse Functions provides complete coverage of inverse functions from Intermediate Algebra and College Algebra courses.