We started by looking at a problem with triangles. Two smaller triangles made up a larger triangle. The larger triangle was a right triangle. Basically, we started finding different angles, and use the law of sines at one point. Then we could use a trigonometric identity.
For another problem, it helped to create a new variable.
We spent a little time on graphs of trigonometric identities and also understanding the domain and range. That included looking at the amplitude and expansion and compression of functions.