Digital Lesson Inverse Trigonometric Functions Inverse Sine Function

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Digital Lesson Inverse Trigonometric Functions

Digital Lesson Inverse Trigonometric Functions

Inverse Sine Function Recall that for a function to have an inverse, it must

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 y = sin x x Sin x has an inverse function on this interval. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2

 Angle whose sine is x Example: This is another way to write arcsin

Angle whose sine is x Example: This is another way to write arcsin x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3

Inverse Cosine Function f(x) = cos x must be restricted to find its inverse.

Inverse Cosine Function f(x) = cos x must be restricted to find its inverse. y y = cos x x Cos x has an inverse function on this interval. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4

 Angle whose cosine is x Example: This is another way to write arccos

Angle whose cosine is x Example: This is another way to write arccos x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5

Inverse Tangent Function f(x) = tan x must be restricted to find its inverse.

Inverse Tangent Function f(x) = tan x must be restricted to find its inverse. y y = tan x x Tan x has an inverse function on this interval. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6

 Angle whose tangent is x The domain of y = arctan x is

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. 7

Graphing Utility: Graph the following inverse functions. Set calculator to radian mode. a. y

Graphing Utility: Graph the following inverse functions. Set calculator to radian mode. a. y = arcsin x – 1. 5 – 2 b. y = arccos x – 1. 5 – c. y = arctan x – 3 3 – Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 8

Graphing Utility: Approximate the value of each expression. Set calculator to radian mode. a.

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. 9