Using Reference Angles to Find Trigonometric Functions

Use reference angles to find all six trigonometric functions of $- \frac{5 π}{6} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The angle between this angle’s terminal side and the x-axis is $\frac{π}{6},$ so that is the reference angle. Since $- \frac{5 π}{6}$ is in the third quadrant, where both $x$ and $y$ are negative, cosine, sine, secant, and cosecant will be negative, while tangent and cotangent will be positive.

$\begin{matrix} cos (- \frac{5 π}{6}) & = - \frac{\sqrt{3}}{2}, sin (- \frac{5 π}{6}) & = - \frac{1}{2}, tan (- \frac{5 π}{6}) & = \frac{\sqrt{3}}{3}, \\ sec (- \frac{5 π}{6}) & = - \frac{2 \sqrt{3}}{3}, csc (- \frac{5 π}{6}) & = −2, cot (- \frac{5 π}{6}) & = \sqrt{3} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use reference angles to find all six trigonometric functions of $- \frac{7 π}{4} .$

How did it go?