Without solving, how do you determine the number of solutions for the equation #sectheta=(2sqrt3)/3# in #-180^circ<=theta<=180^circ#?
So you're really looking at where
Since the cosine function is "even",
So if there is a solution from 0 to
We can readily see that
We know that the range of the cosine function is between -1 and 1, so this is good news, this means that there is a solution (if the value was larger than 1, we would have had zero solution).