rewrite the following expression as an algebraic expression in x: cos(arcsin x)

Question

I have made X to be X/1 but from there I am lost.

Answer 1

draw a triangle, and label angle θ so that

opposite side = x
hypotenuse = 1

so, sinθ = x, so θ = arcin x

Now, label the adjacent leg:√(1-x^2)

so, now you know that cosθ = √(1-x^2)

ta-da -- cos(arcsin x) = √(1-x^2)