Question

what is \\(\frac{5pi}{6}\\) radians converted to degrees? if necessary, round your answer to the nearest degree.\
\\(\bigcirc\\) \\(30^\circ\\)\
\\(\bigcirc\\) \\(90^\circ\\)\
\\(\bigcirc\\) \\(150^\circ\\)\
\\(\bigcirc\\) \\(900^\circ\\)

Explanation:

Step1: Recall radian to degree formula

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

Step2: Substitute the given radian value

Given \( \text{Radians} = \frac{5\pi}{6} \), substitute into the formula:
\( \text{Degrees} = \frac{5\pi}{6} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out:
\( \text{Degrees} = \frac{5}{6} \times 180^\circ \)
Calculate \( \frac{5 \times 180^\circ}{6} = 5 \times 30^\circ = 150^\circ \)

Answer:

C. \( 150^\circ \)