Rewrite tan sin1 w4 as an algebraic expression in w tansin1

Rewrite tan (sin^-1 w/4) as an algebraic expression in w. tan(sin^-1 w/4) =

Solution

recall that tan(u) = sin(u)/cos(u)

tan[arcsin(w/4)] = sin[arcsin(w/4)]/cos[arcsin(w/4)]

sin[arcsin(w/4)] = w/4 trivially

By the pythagorean identity

sin^2(u) + cos^2(u) = 1
w^2/16 + cos^2(u) = 1
cos(u) = sqrt(1 - w^2/16)

tan[arcsin(w/4)] = sin[arcsin(w/4)]/cos[arcsin(w/4)]

tan[arcsin(w/4)] = (w/4)/sqrt(1 - w^2/16)