Question

In the interval [0,27π], how many solutions are there to sinθ=−1/3?

Answer 1

The value -1/3 is in [0;1] : it will necessarily be reached by the sine function, twice, on an interval of the form [0,2Pi] (See a graph to convince yourself : it happens in the [Pi;2Pi] part) . The value of θ at these 2 points is irrelevant.
How many interval of width 2Pi is there between 0 and 27 Pi ? There is 13, plus an additional Pi : therefore, there is 13*2 = 26 solutions to the equation.

Answer 2

The aforementioned graph : http://i.imgur.com/X8WAi.jpg