Using Identities to Evaluate Trigonometric Functions

Because we know the sine and cosine values for these angles, we can use identities to evaluate the other functions.

1. ⓐ
   $\begin{array}{ccc}\hfill \tan (\mathrm{45°})& =& \frac{\sin (\mathrm{45°})}{\cos (\mathrm{45°})}\hfill \\ & =& \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}\hfill \\ & =& 1\hfill \end{array}$
2. ⓑ
   $\begin{array}{ccc}\hfill \sec \left(\frac{5\pi }{6}\right)& =& \frac{1}{\cos \left(\frac{5\pi }{6}\right)}\hfill \\ & =& \frac{1}{-\frac{\sqrt{3}}{2}}\hfill \\ & =& \frac{\mathrm{-2}\sqrt{3}}{1}\hfill \\ & =& \frac{\mathrm{-2}}{\sqrt{3}}\hfill \\ & =& -\frac{2\sqrt{3}}{3}\hfill \end{array}$