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`

Answer 1

(a) `pi/3`

We know
\[\sin^{- 1} \left( \sin{x} \right) = x\]
Now,
\[\theta = \sin^{- 1} \left\{ \sin\left( - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {720}^\circ - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {120}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {180}^\circ - {120}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( \pi - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {60}^\circ \right)\]
\[ = {60}^\circ\]