Question

Pi/6 is the reference angle for: 3pi/6 5pi/6 13pi/6 8pi/6

Answer 1

Answer:

$\frac{5\pi}{6}, \frac{13\pi}{6}$

Step by step

Remember, a reference angle is a positive acute angle that represents an angle θ of any measurement.

a)

$\frac{3\pi}{6}=90^\circ$, then its reference angle is $\frac{\pi}{2}$

b)

$\frac{5\pi}{6}=150^ \circ$ is in the second cuadrant, then its reference angle is $180^ \circ -150^{\circ}=30^{\circ}=\frac{\pi}{6}$

c)

$\frac{13\pi}{6}=390^\circ=360^\circ+30^\circ$, then it is in the first cuadrant and the reference angle is $30^\circ =\frac{\pi}{6}$.

d)

$\frac{8\pi}{6}=240^\circ$ and it is in the third cuadrant, then its reference angle is $240^\circ -180^\circ=60^\circ=\frac{\pi}{3}$