# Find the exact values without a calculator: (a) $\tan \frac{11\pi }6$ (b) $\sec \frac{-3\pi}4$ (c) $\cot \frac{-5 \pi}3$

Okay I know the unit circle back and forth, but I get confused when I am asked to find answers that do not refer to sine and cosine.

For example, I am ask to evaluate $\tan \frac{11\pi }6$. Since tan is sine / cosine do I find the sine value at $11 \pi$ and the cosine value at 6?

What is the thought process I should be using?

"tan is sine / cosine" means that to find the value of tangent you find the values of sine and of cosine at that same value, then you divide the sine and cosine. So, you use $$\tan \frac{11\pi}6 = \frac{{\sin \frac{{11\pi }}{6}}}{{\cos \frac{{11\pi }}{6}}}$$
Similarly, $$\sec \frac{{ - 3\pi }}{4} = \frac{1}{{\cos \frac{{ - 3\pi }}{4}}}$$ and $$\cot\frac{{ - 5\pi }}{3} = \frac{{\cos \frac{{ - 5\pi }}{3}}}{{\sin \frac{{ - 5\pi }}{3}}}$$