If sin y = cos 3y, determine an exact value for angle y.

We have to find y such that sin y = cos
3y.

We know that sin(y) = cos(pi/2-y),so we can convert the
given equation to:

sin(y) = cos(pi/2-y) =
cos(3y)

We now equate pi/2 - y and
3y

pi/2 - y = 3y

=>
pi/2 = 3y + y

=> 4y =
pi/2

=> y =
pi/8

Therefore y = pi/8 +
2*n*pi