Question

Let x equals negative 31 times pi over 6 periodDetermine the reference angle of x

Answer 1

Given :

$x=-\frac{31\pi}{6}$$\text{Substitute }\pi=180^o,\text{ we get }$

$x=-\frac{31\times180^o}{6}$

$x=-31\times30^o$

$x=-930^o$

$x=-930^o=-720-210$

$x=-930^o=-2\times360-180-30$

After two full rotating, and 180 degrees, the angle is 30 degrees in 3 rd quadrant.

The reference angle is the angle that the given angle makes with the x-axis.

Hence the required reference angle is 30 degrees.