Question

Write the value of sin⁻¹ (sin 1550°).

Answer 1

We know that 

\[\sin^{- 1} \left( \sin{x} \right) = x\]

Now,

\[\sin^{- 1} \left( \sin {1550}^\circ \right) = \sin^{- 1} \left\{ \sin\left( {1620}^\circ - {1550}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( {1620}^\circ - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {70}^\circ \right)\]
\[ = {70}^\circ \]
\[\]

∴ \[\sin^{- 1} \left( \sin {1550}^\circ \right) = {70}^\circ\]