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

Textbook Question

Chapter 4, 4.7 - Problem 66 - Precalculus (3rd Edition, Ron Larson).
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kspcr111 | In Training Educator

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`sin(arctan(x))`

let `theta = arctan(x)`

=> `tan(theta)=x= x/1`

by using the right triangle we get the hypotenuse is `= sqrt(1+x^2)`

so `sin(theta) = x/(sqrt(1+x^2))`

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