Inverse Trigonometric Functions Digital Lesson Inverse Trigonometric Functions

Inverse Sine Function Recall that for a function to have an inverse, it must be a one-to-one function and pass the Horizontal Line Test. f(x) = sin x does not pass the Horizontal Line Test and must be restricted to find its inverse. y x y = sin x Sin x has an inverse function on this interval. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Sine Function

Example: Angle whose sine is x This is another way to write arcsin x.   Angle whose sine is x     Example: This is another way to write arcsin x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Sine Function

Inverse Cosine Function f(x) = cos x must be restricted to find its inverse. y x y = cos x Cos x has an inverse function on this interval. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Cosine Function

Inverse Cosine Function   Angle whose cosine is x     Example: This is another way to write arccos x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Cosine Function

Inverse Tangent Function f(x) = tan x must be restricted to find its inverse. y x y = tan x Tan x has an inverse function on this interval. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Tangent Function

Inverse Tangent Function   Angle whose tangent is x The domain of y = arctan x is .   Example: This is another way to write arctan x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Tangent Function

Graphing Utility: Graphs of Inverse Functions Graphing Utility: Graph the following inverse functions. Set calculator to radian mode. –1.5 1.5 –  a. y = arcsin x –1.5 1.5 2 – b. y = arccos x –3 3  – c. y = arctan x Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Graphing Utility: Graphs of Inverse Functions

Graphing Utility: Inverse Functions Graphing Utility: Approximate the value of each expression. Set calculator to radian mode. a. cos–1 0.75 b. arcsin 0.19 c. arctan 1.32 d. arcsin 2.5 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Graphing Utility: Inverse Functions