Question

What is the reference angle and cosine of StartFraction 7 pi Over 6 EndFraction ?

Answer 1

Answer:

$\frac{\pi}{6}$ radians

$cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}$

Step-by-step explanation:

A reference angle is an acute angle between the terminal arm/terminal side and the x-axis. In this case, the reference angle is $\frac{7\pi}{6}-\pi=\frac{\pi}{6}$.

As for $cos(\frac{7\pi}{6})$, we can identify the value of it using the unit circle as attached below. Recall that points on the unit circle are defined as $(cos(\theta),sin(\theta))$, so $cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}$.