Question

convert $\frac{7\pi}{2}$ radians to degrees. (1 point)
$\bigcirc$ 630 degrees
$\bigcirc$ 520 degrees
$\bigcirc$ 645 degrees
$\bigcirc$ 720 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 radians

We are given \( \frac{7\pi}{2} \) radians. Substitute this into the formula:
\( \text{Degrees} = \frac{7\pi}{2} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out:
\( \text{Degrees} = \frac{7}{2} \times 180^\circ \)
Calculate \( \frac{7}{2} \times 180^\circ \):
\( \frac{7 \times 180^\circ}{2} = 7 \times 90^\circ = 630^\circ \)

Answer:

630 degrees (corresponding to the first option: 630 degrees)