The value of sin^-1 (cos (53 Π)/5 ) is

Correct answer: (D) -(Π)/10. Given that, sin^-1 (cos (53 π)/5 ) =sin^-1 \cos (10 Π+(3 π)/5 ) \ =sin^-1 (cos (3 π)/5 ) =sin^-1 (cos ((Π)/2+(Π)/10 ) ) =sin^-1 (-sin ((Π)/10 ) ) =sin^-1 (sin (-(Π)/10 ) )=(-Π)/10

Q64 / 180 · KCET 2016 · Mathematics

The value of \( \sin ^{-1}\left(\cos \frac{53 \Pi}{5}\right) \) is

A
\( 3 \frac{\Pi}{5} \)
B
\(-3 \frac{\Pi}{5} \)
C
\( \frac{\Pi}{10} \)
Correct answer
D
\( -\frac{\Pi}{10} \)

Solution

Given that, \( \sin ^{-1}\left(\cos \frac{53 \pi}{5}\right) \) \( =\sin ^{-1}\left\{\cos \left(10 \Pi+\frac{3 \pi}{5}\right)\right\} \) \( =\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right) \) \( =\sin ^{-1}\left(\cos \left(\frac{\Pi}{2}+\frac{\Pi}{10}\right)\right) \) \( =\sin ^{-1}\left(-\sin \left(\frac{\Pi}{10}\right)\right) \) \( =\sin ^{-1}\left(\sin \left(-\frac{\Pi}{10}\right)\right)=\frac{-\Pi}{10} \)

Hence, the correct answer is option: 'D'.

The value of \( \sin ^{-1}\left(\cos \frac{53 \Pi}{5}\right) \) is

Solution

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