Answer:
The reference angle of [tex]\frac{2\pi}{3}[/tex] is [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2\pi}{3}[/tex]
Required
Which represent its reference angle
The very first step is to determine the quadrant of the given angle
For better understanding;
Convert [tex]\frac{2\pi}{3}[/tex] to degrees
[tex]\frac{2\pi}{3}[/tex] = [tex]\frac{2}{3} * 180[/tex]
[tex]\frac{2\pi}{3}[/tex] = [tex]\frac{2 * 180}{3}[/tex]
[tex]\frac{2\pi}{3}[/tex] = [tex]\frac{360}{3}[/tex]
[tex]\frac{2\pi}{3}[/tex] = [tex]120[/tex]
120 degrees in in the second quadrant; Hence, [tex]\frac{2\pi}{3}[/tex] is in the second quadrant
The reference angle of [tex]\frac{2\pi}{3}[/tex] is calculated using the following formula;
[tex]\pi - \frac{2\pi}{3}[/tex]
Rewrite [tex]\pi[/tex]
[tex]\pi - \frac{2\pi}{3} = \frac{3\pi}{3} - \frac{2\pi}{3}[/tex]
Take LCM
[tex]\pi - \frac{2\pi}{3} = \frac{3\pi - 2\pi}{3}[/tex]
[tex]\pi - \frac{2\pi}{3} = \frac{\pi}{3}[/tex]
Hence, the reference angle of [tex]\frac{2\pi}{3}[/tex] is [tex]\frac{\pi}{3}[/tex]
