Question

The degree measure of $\frac{\pi}{32}$ is equal to

• A. $5^\circ 30' 20''$
• B. $5^\circ 37' 30''$
• C. $5^\circ 37' 20''$
• D. $4^\circ 30' 30''$

Answer 1

Answer: (B)

$5^\circ 37' 30''$

Answer 2

we know that π radians is equivalent to 180 degrees.
So,$\frac{\pi}{32}$ radians can be converted to degrees as follows:
$\left(\frac{\pi}{32}\right) \times \left(\frac{180}{\pi}\right) = \frac{180}{32} \text{ degrees} = 5.625 \text{ degrees}$
Since 0.625 degrees is equal to $0.625 \times 60 = 37.5 \text{ minutes}$, we have:
5.625 degrees = 5 degrees 37.5 minutes.
To express the minutes in terms of minutes and seconds, we can calculate $0.5 \times 60 = 30 \text{ seconds}$
Therefore, the degree measure of $\frac{\pi}{32}$ is equal to 5 degrees 37 minutes 30 seconds.
Hence, the correct option is (B) $5^\circ \ 37' \ 30''$.