Question

question
convert the angle ( \frac{7pi}{3} ) radians to degrees.

answer attempt 1 out of 2

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 measure

We are given \( \frac{7\pi}{3} \) radians. Substitute this into the formula:
\( \text{Degrees} = \frac{7\pi}{3} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out:
\( \text{Degrees} = \frac{7}{3} \times 180^\circ \)
Calculate \( \frac{7 \times 180^\circ}{3} \). First, divide 180 by 3: \( 180 \div 3 = 60 \). Then multiply by 7: \( 7 \times 60^\circ = 420^\circ \)

Answer:

\( 420^\circ \)