Question

how many degrees are equivalent to (\frac{4pi}{15}) radians? 48° 24° 96° 675°

Explanation:

Step1: Recall the radian to degree 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 into the formula

We are given \( \frac{4\pi}{15} \) radians. Substitute this into the formula:
\( \text{Degrees} = \frac{4\pi}{15} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out:
\( \text{Degrees} = \frac{4}{15} \times 180^\circ \)
Calculate \( \frac{4 \times 180^\circ}{15} \). First, \( 180 \div 15 = 12 \), then \( 4 \times 12 = 48 \). So we get \( 48^\circ \)

Answer:

\( 48^\circ \) (corresponding to the option "48°")