Question

convert \\(\frac{7\pi}{21}\\) to degrees.
a \\(30^\circ\\)
b \\(60^\circ\\)
c \\(90^\circ\\)
d \\(120^\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 \( \frac{7\pi}{21} \) radians. First, simplify \( \frac{7\pi}{21}=\frac{\pi}{3} \) (by dividing numerator and denominator by 7). Then substitute into the formula: \( \frac{\pi}{3} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out, and we have \( \frac{180^\circ}{3}=60^\circ \)

Answer:

B. \( 60^\circ \)