Question

convert \\(\frac{5\pi}{6}\\) radians to degrees. (1 point)
\\(\bigcirc\\) 30 degrees
\\(\bigcirc\\) 90 degrees
\\(\bigcirc\\) 120 degrees
\\(\bigcirc\\) 150 degrees

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given radian value

We are given \( \frac{5\pi}{6} \) radians. Substitute this into the formula:
\( \text{Degrees} = \frac{5\pi}{6} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out:
\( \text{Degrees} = \frac{5}{6} \times 180^\circ \)
Calculate \( \frac{5}{6} \times 180 \):
\( 180 \div 6 = 30 \), then \( 30 \times 5 = 150 \)
So, \( \frac{5\pi}{6} \) radians is \( 150^\circ \)

Answer:

150 degrees (corresponding to the option: 150 degrees)