`cos(arcsin(2x))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

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Textbook Question

Chapter 4, 4.7 - Problem 67 - Precalculus (3rd Edition, Ron Larson).
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balajia's profile pic

balajia | College Teacher | (Level 1) eNoter

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`cos(sin^(-1)(2x)) = cos(cos^(-1)(sqrt(1-(2x)^2)))`



kspcr111's profile picture

kspcr111 | In Training Educator

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let `theta = arcsin(2x)`

so we need to find `cos(theta)`

As ` theta = arcsin(2x)`

`sin(theta)= 2x = (2x)/1 = (opposite side) / (hypotenuse)`

by using the right triangle we get the hypotenuse as =1

so, the adjacent side = sqrt(hypotenuse ^2 - opposite side^2)

                                `= sqrt(1-(2x)^2)`


so` cos(theta)` = adjacent side/hypotenuse = `sqrt(1-4x^2)/1`

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