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

Textbook Question

Chapter 4, 4.7 - Problem 74 - Precalculus (3rd Edition, Ron Larson).
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vnessawong21 | (Level 1) Salutatorian

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u = sin(v)

cos(v) = sqrt(1-(sin(v))^2) = sqrt(1-u^2)

But v = arcsin(u), 

therefore cos(arcsin(u)) = sqrt(1-u^2). 

Next replace u with (x-h)/r to get:

cos(arcsin((x-h)/r)) = sqrt(1-(x-h)^2/r^2).

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