Answer:
The exact value
[tex]sin^{-1} (\frac{-1}{2} ) = \frac{7\pi }{6}[/tex] = 210°
Step-by-step explanation:
Step(i):-
Given that the inverse trigonometry
[tex]sin^{-1} (\frac{-1}{2} )[/tex]
We know that the sine function has negative in third quadrant
[tex]sin^{-1} (\frac{-1}{2} ) = sin^{-1} ( sin (\pi +\frac{\pi }{6} )[/tex]
We have to use trigonometric formula
[tex]sin^{-1} ( sin (x)) = x[/tex]
Step(ii):-
[tex]sin^{-1} (\frac{-1}{2} ) = sin^{-1} ( sin (\pi +\frac{\pi }{6} ) = \pi +\frac{\pi }{6}[/tex]
= [tex]\frac{6\pi +\pi }{6} = \frac{7\pi }{6}[/tex]
Final answer:-
The exact value
[tex]sin^{-1} (\frac{-1}{2} ) = \frac{7\pi }{6}[/tex]