Rewrite the trigonometric expression algebraically. cos(sin-1(1/u))

Question

 assume that u is greater than 1

Answer 1

Let's confine ourselves to the first quadrant.

The inverse sine function gives us an angle; let θ = sin^-1(1/u), i.e. sin θ = 1/u.

Draw a right triangle and call one of the acute angles θ.  

Label the hypotenuse u and label the side opposite θ  as having length 1.

Then the third side must be √(u²-1).

cos θ can then be computed using the ratio of the third side to the hypotenuse.