Calculus II Notes 7.6

Calculus II Notes 7.6 - Calculus II-Stewart Dr. Berg Spring...

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Calculus II- Stewart Dr. Berg Spring 2010 Page 1 7.6 7.6 Inverse Trig Functions Inverses The inverses of the trig functions are an important addition to our toolbox. Recall that f 1 ( x ) = y if and only if f ( y ) = x , and that to be invertible, a function must be one- to-one (pass the horizontal line test). To make the trig functions invertible, we must restrict the domain to an appropriate interval. Trig Inverses Definition y = sin 1 x if and only if x = sin y and π 2 y 2 . Note: 1) Since the domain of the inverse function is the range of the inverted function, the domain of the arcsine is [ 1,1] . 2) sin 1 sin x ( ) = x if 2 x 2 . 3) sin sin 1 x ( ) = x if 1 x 1 . 4) It is useful to think of arcsin x as the angle whose sine is x . Example A a) sin 1 1/2 ( ) = /6 since sin ( ) = . b) sin 1 1/ ( ) = /4 since sin ( ) = .

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Calculus II- Stewart Dr. Berg Spring 2010 Page 2 7.6 Example B Evaluate tan(arcsin(1/4)). Solution : We use a right triangle appropriately labeled to solve this. Observe that sin θ = 1/4 so that sin 1 ( ) = , and tan = 1/ b , so we must evaluate b .
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This note was uploaded on 02/28/2010 for the course M 56495 taught by Professor Berg during the Spring '10 term at University of Texas.

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Calculus II Notes 7.6 - Calculus II-Stewart Dr. Berg Spring...

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