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Question
Write the value of sin−1 (sin 1550°).
Solution
We know that
\[\sin^{- 1} \left( \sin{x} \right) = x\]
Now,
\[\sin^{- 1} \left( \sin {1550}^\circ \right) = \sin^{- 1} \left\{ \sin\left( {1620}^\circ - {1550}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( {1620}^\circ - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {70}^\circ \right)\]
\[ = {70}^\circ \]
\[\]
∴ \[\sin^{- 1} \left( \sin {1550}^\circ \right) = {70}^\circ\]
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