Question

convert \\(\frac{5\pi}{3}\\) radians to degrees.

a. \\(225^\circ\\)

b. \\(240^\circ\\)

c. \\(300^\circ\\)

d. \\(108^\circ\\)

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 \( \frac{5\pi}{3} \) radians. Substitute this into the formula:
\( \text{Degrees} = \frac{5\pi}{3} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out:
\( \text{Degrees} = \frac{5}{3} \times 180^\circ \)
Calculate \( \frac{5}{3} \times 180^\circ \):
\( 5 \times 60^\circ = 300^\circ \)

Answer:

C. \( 300^\circ \)