Correct option is (D) \(\frac \pi {32}\)
\(30'' = (\frac12)'\)
\(\therefore 37'30'' = (37 \frac 12)' = (\frac{75}2)'\)
\(= (\frac{75}2 \times \frac 1{60})°\)
\(= (\frac 58)°\)
\(\therefore 5°37'30'' = (5 \frac 58)° =(\frac{45}8)°\)
\(=( \frac{45}{8} \times \frac \pi {180})^c\)
\(= (\frac \pi{32})^c\)
