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

The Correct Option is B

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) \(5^\circ \ 37' \ 30''\).