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PP Section 8.5

# PP Section 8.5 - The Inverse Trigonometric Functions...

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The Inverse Trigonometric Functions

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Inverse Functions Let f denote a one-to-one function y = f (x) . The inverse of f , denoted f -1 , is a function such that f -1 ( f ( x )) = x for every x in the domain f and f ( f -1 ( x )) = x for every x in the domain of f -1 . The trigonometric functions are NOT one-to-one. To be able to define inverse trigonometric functions, we need to start by restricting their domains.
2 2 ), sin( π π - = x x y To get a one-to-one function, we selected an interval for x that includes 0 and over which the entire range of sine is covered. This version of the sine function has an inverse function.

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The Inverse Sine Function means where and y x x y y x = = - - - sin sin 1 2 2 1 1 π π ( 29 sin sin - = - 1 2 u u u where 2 π π ( 29 sin sin - = - 1 1 1 v v v where
Characteristics of y x = - sin 1 Domain of is the Range of y x y x x = = - ≤ - sin sin : 1 1 1 Range of is the Domain of y x y x y = = - - sin sin : 1 2 2 π π

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) ( sin 1 x y - = 2 2 ), sin( π π - = x x y Graphs
Example = - 2 3 sin of e exact valu the Find 1 y 2 2 2 3 sin 1 π θ π θ - = - 2 2 2 3 sin π θ π θ - = 3 π θ = = y

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PP Section 8.5 - The Inverse Trigonometric Functions...

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