inverse trigonometric question

Question

Write the expression in algebraic form.

 

sin(cos−1 x)

Answer 1

let cos θ = x

then cos^-1x = θ

 

draw a rt triangle with hypotenuse 1, acute angle θ, and the adjacent side = x;

then the opposite side is √(1-x²).

 

sin θ = √(1-x²), which is your desired answer.