### Home > APCALC > Chapter 1 > Lesson 1.2.1 > Problem1-26

1-26.

What is the exact value of each of the following trig expressions?

1. $\sin\left(\frac{5\pi}{3}\right)$

Recall your unit circle, or the graph of $f(x) = \sin x$.

$\text{Since reference point: sin}\frac{\pi}{3}=\frac{\sqrt{3}}{2},$

$\text{sin}\frac{5\pi}{3}\text{ will equal EITHER}\frac{\sqrt{3}}{2}\text{ or }-\frac{\sqrt{3}}{2}.$

Which one?

2. $\tan\left(\frac{7\pi}{6}\right)$

$\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$

$\text{tan}\frac{7\pi }{6}=\frac{\text{sin}\frac{7\pi }{6}}{\text{cos}\frac{7\pi }{6}}= \underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$

Now simplify!

3. $\sec\left(\frac{5\pi}{4}\right)$

$\text{sec}x=\frac{1}{\text{cos}x}$

$\text{sec}\frac{5\pi }{4}=\frac{1}{\text{cos}\frac{5\pi }{4}}= \underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$

Now simplify!

4. $\csc\left(\pi\right)$

$\text{csc}x=\frac{1}{\text{sin}x}$

Careful! $\sin π = 0$. What does that mean about the reciprocal of $\sin x$.