15: The domain is D( f ) = ℝ.
The derivative is

Critical points: The equation f ′(x) = 0 has solutions x = π/2 + kπ, x = π/6 + 2kπ, and x = 5π/6 + 2kπ.
There are no points in D( f ) where the derivative does not exist.

The function is 2π-periodic. Draw a picture to see how the critical points fit. Determine monotonicity and local extrema using a chart, it is enough to check on two neighboring periods to see what is happening.

Next hint
Answer