Write each trigonometric expression as an algebraic expression in u, for u 7 0. sin (arc cos u)

Answer 1

To express sin (arc cos u) as an algebraic expression in u, we need to use the identity sin^2 x + cos^2 x = 1.

Given that we have arc cos u, let's assume that the angle of the arc cos is x. This means that cos x = u.

Using the identity mentioned earlier, we can find sin x:

sin^2 x + cos^2 x = 1
sin^2 x + u^2 = 1
sin^2 x = 1 - u^2
sin x = √(1 - u^2)

Therefore, sin (arc cos u) can be expressed as:

sin (arc cos u) = √(1 - u^2)