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Question
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Solution
We know that
\[\sin^{- 1} \left(\sin{x} \right) = x\]
Now,
\[\sin^{- 1} \left\{ \sin\left( - {600}^\circ \right) \right\} = \sin^{- 1} \left\{ \sin\left( {720}^\circ - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {120}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {180}^\circ - {120}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( \pi - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {60}^\circ \right)\]
\[ = {60}^\circ\]
∴ \[\sin^{- 1} \left\{ \sin\left( - {600}^\circ \right) \right\} = {60}^\circ\]
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