PP Section 8.5 - The Inverse Trigonometric Functions...

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Unformatted text preview: The Inverse Trigonometric Functions 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( - = 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. The Inverse Sine Function means where and y x x y y x = =- - - sin sin 1 2 2 1 1 ( 29 sin sin- =- 1 2 u u u where 2 ( 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 ) ( sin 1 x y- = 2 2 ), sin( - = x x y Graphs Example =- 2 3 sin of e exact valu the Find 1 y 2 2 2 3 sin 1 - =- 2 2 2 3 sin - = 3 = = y .....
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 8.5 - The Inverse Trigonometric Functions...

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