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Question
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
Options
`pi/3`
`pi/2`
`(2pi)/3`
`-(2pi)/3`
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Solution
(a) `pi/3`
We know
\[\sin^{- 1} \left( \sin{x} \right) = x\]
Now,
\[\theta = \sin^{- 1} \left\{ \sin\left( - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {720}^\circ - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {120}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {180}^\circ - {120}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( \pi - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {60}^\circ \right)\]
\[ = {60}^\circ\]
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