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The measure of an angle in degrees, grades and radians be D,G and C respectively then the relation between them
$\frac{D}{90} = \frac{G}{100} = \frac{2 C}{π} b u t 1^{c} = {(\frac{180}{π})}^{°} = 57 ° .17' 44.8 "$ then the value of $\cos 1^{c}$ is

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$< \frac{1}{2}$

$\frac{1}{2}$

$> \frac{1}{2}$

answer is C.

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Detailed Solution

$\begin{array}{l} 1^{c} = 57 °, 17', 44.8 " < 60 ° \\ ∴ \cos 1^{c} > \cos 60 ° = \frac{1}{2} \\ H e n c e \cos 1^{c} > \frac{1}{2} \end{array} (∵ \cos i s d e c r e a \sin g i n (0, \frac{π}{2}))$

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