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Find the value of the following:

                  sin\left[ {arc{\rm{ cos}}\left( {{\rm{ - }}\frac{{\rm{1}}}{{\rm{2}}}} \right)} \right]

Option: 1

\frac{1}{2}


Option: 2

-\frac{1}{2}


Option: 3

\frac{\sqrt3}{2}


Option: 4

-\frac{\sqrt3}{2}


Answers (1)

best_answer

As we learnt

 

Important Results of Inverse Trigonometric Functions -

 

\cos ^{-1}\left ( -x \right )= \pi - \cos ^{-1}x

-

 

 

\sin\left[ {arc{\rm{ cos}}\left( {{\rm{ - }}\frac{{\rm{1}}}{{\rm{2}}}} \right)} \right] = \sin \left[ {\pi - {{\cos }^{ - 1}}\frac{1}{2}} \right]            \left[\because {{{\cos }^{ - 1}}\left( { - \frac{1}{2}} \right) = \pi - {{\cos }^{ - 1}}\frac{1}{2}} \right]

= \sin\left[ {\pi - \frac{\pi }{3}} \right] = \sin \frac{{2\pi }}{3} = \frac{{\sqrt 3 }}{2}

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chirag

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