Write each trigonometric expression as an algebraic expression in u, for u 7 0. cos (arc sin u)
To write the trigonometric expression cos(arc sin u) as an algebraic expression in u, we need to use the inverse trigonometric function and the Pythagorean identity.
1. Begin by finding sin(u) using the inverse sine function (arc sin u):
sin(u) = u
2. Use the Pythagorean identity to find the value of cos(u):
cos(u) = √(1 - sin^2(u))
cos(u) = √(1 - u^2)
Therefore, the algebraic expression for cos(arc sin u) is √(1 - u^2).