cos(sin-1(8u))

Question

Rewrite the trigonometric expression as an algebraic expression

Answer 1

Let θ = sin^-1(8u).  Then sinθ = 8u

 

Draw a right triangle with acute angle θ.  label the side opposite θ as 8u and label the hypotenuse as 1 (so, sinθ = 8u/1= 8u).  By the Pythagorean Theorem, the side adjacent to θ is √(1 - 64u²).

 

So, cos(sin^-1(8u)) = cosθ = √(1-64u²)/1 = √(1-64u²)