Question

Which represents the reference angle for 2pi/3

Answer 1

Answer:

The reference angle of $\frac{2\pi}{3}$ is $\frac{\pi}{3}$

Step-by-step explanation:

Given

$\frac{2\pi}{3}$

Required

Which represent its reference angle

The very first step is to determine the quadrant of the given angle

For better understanding;

Convert $\frac{2\pi}{3}$ to degrees

$\frac{2\pi}{3}$ = $\frac{2}{3} * 180$

$\frac{2\pi}{3}$ = $\frac{2 * 180}{3}$

$\frac{2\pi}{3}$ = $\frac{360}{3}$

$\frac{2\pi}{3}$ = $120$

120 degrees in in the second quadrant; Hence, $\frac{2\pi}{3}$ is in the second quadrant

The reference angle of $\frac{2\pi}{3}$ is calculated using the following formula;

$\pi - \frac{2\pi}{3}$

Rewrite $\pi$

$\pi - \frac{2\pi}{3} = \frac{3\pi}{3} - \frac{2\pi}{3}$

Take LCM

$\pi - \frac{2\pi}{3} = \frac{3\pi - 2\pi}{3}$

$\pi - \frac{2\pi}{3} = \frac{\pi}{3}$

Hence, the reference angle of $\frac{2\pi}{3}$ is $\frac{\pi}{3}$