KCET · Maths · Trigonometric Ratios & Identities
The degree measure of \(\frac{\pi}{32}\) is equal to
- A \(5^{\circ} 30^{\prime} 20^{\prime \prime}\)
- B \(5^{\circ} 37^{\prime} 20^{\prime \prime}\)
- C \(5^{\circ} 37^{\prime} 30^{\prime \prime}\)
- D \(4^{\circ} 30^{\prime} 30^{\prime \prime}\)
Answer & Solution
Correct Answer
(C) \(5^{\circ} 37^{\prime} 30^{\prime \prime}\)
Step-by-step Solution
Detailed explanation
Given, angle in radian \(=\frac{\pi}{32}\)
\[
\begin{aligned}
\text { Degree measure } & =\frac{180}{\pi} \times \text { radian measure } \\
& =\frac{180}{\pi} \times \frac{\pi}{32}=\left(\frac{45}{8}\right)^{\circ}=\left(5 \frac{5}{8}\right)^{\circ} \\
& =5^{\circ}\left(\frac{5}{8} \times 60\right)^{\prime}=5^{\circ}\left(\frac{75}{2}\right)^{\prime} \\
& =5^{\circ} 37^{\prime}\left(\frac{1}{2} \times 60\right)^{\prime \prime}=55^{\prime} 37^{\prime} 30^{\prime \prime}
\end{aligned}
\]
\[
\begin{aligned}
\text { Degree measure } & =\frac{180}{\pi} \times \text { radian measure } \\
& =\frac{180}{\pi} \times \frac{\pi}{32}=\left(\frac{45}{8}\right)^{\circ}=\left(5 \frac{5}{8}\right)^{\circ} \\
& =5^{\circ}\left(\frac{5}{8} \times 60\right)^{\prime}=5^{\circ}\left(\frac{75}{2}\right)^{\prime} \\
& =5^{\circ} 37^{\prime}\left(\frac{1}{2} \times 60\right)^{\prime \prime}=55^{\prime} 37^{\prime} 30^{\prime \prime}
\end{aligned}
\]
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