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?


You certainly should NOT be using the "thought process" that "tan(a/b}= sin(a)/cos(b)}" because that is NOT true!

  • $\begingroup$ This is perhaps better as a comment than an answer. $\endgroup$ – Dilip Sarwate Jun 6 '15 at 13:23

"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 $$\cot\frac{{ - 5\pi }}{3} = \frac{{\cos \frac{{ - 5\pi }}{3}}}{{\sin \frac{{ - 5\pi }}{3}}}$$

Since you say you "know the unit circle back and forth" you should be able to find each reference angle, find the sine and cosine for that reference angle, calculate your desired trig ratio, then give that ratio the proper sign given the quadrant of the original angle. Ask if you did not understand that brief summary. Good luck!


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