Question

what is the equivalent degree measure of $-\frac{11\pi}{12}$ radians written in simplest terms?\
\\( -\frac{11\pi^2}{2160} \\)\
\\( -165^{\circ} \\)\
\\( -\frac{1980^{\circ}}{12} \\)\
\\( 165^{\circ} \\)

Explanation:

Step1: Recall radian to degree conversion

To convert radians to degrees, we use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \).

Step2: Apply the formula to \(-\frac{11\pi}{12}\)

Substitute the given radian measure into the formula:

$$ -\frac{11\pi}{12} \times \frac{180^\circ}{\pi} $$

The \(\pi\) terms cancel out:

$$ -\frac{11}{12} \times 180^\circ $$

Step3: Calculate the product

First, simplify \(\frac{180}{12} = 15\). Then multiply by 11: \( 11 \times 15 = 165 \). So the result is \(-165^\circ\).

Answer:

\(-165^\circ\) (corresponding to the option: \(-165^\circ\))