Y=sin(x)

let X~uniform[0,pi/2]

compute density of fy(y) for Y.

my attempt

------------

arcsin(Y) = X

fx(arcsinY)

-------------- = sqrt(1-y^2) * fx(arcsinY)

(1/sqrt(1-y^2))

then

/\ arcsin(pi/2) sqrt(1-y^2) * fx(arcsinY) dy

\

.\

\/ arcsin(0)

/\ infinity sqrt(1-y^2) * fx(arcsinY) dy

\

.\

\/ 0

and i am stuck here as i cannot evaluate this, i probably did something wrong earlier...