• $\mathrm{Given}:\sin^{-1}(e^{i\theta})$
• $Let \sin^{-1}(e^{i\theta}) = x + iy$

$e^{i\theta}= \sin (x +iy)$

$\cos\theta + i\sin\theta = \sin x\ \cos\ hy + i\cos x\ \sin\ hy$

• Comparing real and imaginary parts,

$\cos \theta = \sin x\ \cos\ hy\cdots \mathrm{Equation \ 1}$

$\sin x= \dfrac{\cos\theta}{\cos h y}$

$\sin \theta = \cos x\ \sin …