Find $\sec (-300^\circ).$
I recall that $\sec (\theta) = \frac{1}{\cos (\theta)}$ and that $\cos (-\theta) = \cos (\theta)$ by the evenness of cosine. So $\sec (-300^\circ) = \frac{1}{\cos (-300^\circ)} = \frac{1}{\cos (300^\circ)}$. To find $\cos (300^\circ)$, I use the unit circle and the reference angle of $60^\circ$. I know that $\cos (60^\circ) = \frac{1}{2}$ and that $\cos (300^\circ)$ is positive because it is in the fourth quadrant. So $\cos (300^\circ) = \frac{1}{2}$. Therefore, $\sec (-300^\circ) = \frac{1}{\cos (300^\circ)} = \frac{1}{\frac{1}{2}} = 2$. 