This is part of an exercise to work with the proofs of the sum of angles, either sin(x + y) or in this case cos(x + y).
The solution steps declare BC = sin(y) without any explanation. I guessed at it correctly, but I can't figure out how the steps to derive the answer with any sort of mathematical rigor.
http://home.comcast.net/~yoyotweak/images/BC%20sin%20y.jpg
Amended content:
http://home.comcast.net/~yoyotweak/images/BC_sin_y_options.jpg
Look at the right triangle OBC. The angle opposite $BC$ has measure $\pi - y$. Since $OC$ has unit length, $$BC = \sin(\pi - y) = \sin \pi \cos y - \cos \pi \sin y = 0(\cos y) - (-1)(\sin y) = \sin y.$$