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Inverse Trigonometric Functions
Digital Lesson Inverse Trigonometric Functions
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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
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The range of y = arcsin x is [–/2 , /2].
The inverse sine function is defined by y = arcsin x if and only if sin y = x. Angle whose sine is x The domain of y = arcsin x is [–1, 1]. The range of y = arcsin x is [–/2 , /2]. Example: This is another way to write arcsin x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Sine Function
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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
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Inverse Cosine Function
The inverse cosine function is defined by y = arccos x if and only if cos y = x. Angle whose cosine is x The domain of y = arccos x is [–1, 1]. The range of y = arccos x is [0 , ]. Example: This is another way to write arccos x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Cosine Function
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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
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Inverse Tangent Function
The inverse tangent function is defined by y = arctan x if and only if tan y = x. Angle whose tangent is x The domain of y = arctan x is The range of y = arctan x is [–/2 , /2]. Example: This is another way to write arctan x. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Inverse Tangent Function
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Example: Evaluating Composition of Functions
y 3 u 2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Evaluating Composition of Functions
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Deriving Inverse Trig Fuctions
Tips to remember: If it starts with ‘c’, make it negative!
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Deriving Inverse Trig Fuctions
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Deriving Inverse Trig Fuctions
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Another way to write inverse functions
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Spotlight Search… Copyright © by Houghton Mifflin Company, Inc. All rights reserved.
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…Using inverse trig functions:
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