Question

What is the equivalent degree measure of - 11 π /12 radians written in simplest terms?165°- 165°-11 π^2/2160-1980°/12

Answer 1

To answer this question, we need to remember the conversion formula from radians to degrees. This formula is as follows:

$\frac{180}{\pi}(\text{rad)}=\text{degrees}$

We have, in this case, the following measure in radians:

$-\frac{11\pi}{12}$

We can see that the measure is negative (the measure is in a clockwise direction), and we will have the angle in degrees, also, in a clockwise direction (negative). Then we have:

$\begin{gathered} \frac{180}{\pi}(-\frac{11}{12}\pi)=-(\frac{180}{12})(11)(\frac{\pi}{\pi})=-(15)(11)(1)=-165 \\ \end{gathered}$

Therefore, in summary, the degree measure of - 11 π /12 is equivalent to - 165° (second option).