A) \[{{\left( \frac{\pi }{8} \right)}^{c}}\]
B) \[{{\left( \frac{\pi }{12} \right)}^{c}}\]
C) \[{{\left( \frac{\pi }{18} \right)}^{c}}\]
D) \[{{\left( \frac{\pi }{32} \right)}^{c}}\]
Correct Answer: D
Solution :
\[30''\left( \frac{30}{60} \right)'=\frac{1}{2}\] \[\because \,\,37'30\] \[''=\] \[\left( 37\frac{1}{2} \right)'=\left( \frac{75}{2} \right)'=\left( \frac{75}{2}\times \frac{1}{60} \right){}^\circ =\left( \frac{5}{8} \right){}^\circ \] \[\because 5{}^\circ 37'30''\] \[\left( 5\frac{5}{8} \right){}^\circ =\left( \frac{45}{8} \right){}^\circ ={{\left( \frac{45}{8}\times \frac{\pi }{180} \right)}^{c}}={{\left( \frac{\pi }{32} \right)}^{c}}\]
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