Question

find exact value for f(x)=sin^-1(-1/2)

Answer 1

Answer:

The exact value

  $sin^{-1} (\frac{-1}{2} ) = \frac{7\pi }{6}$  =  210°

Step-by-step explanation:

Step(i):-

Given that the inverse trigonometry

          $sin^{-1} (\frac{-1}{2} )$

We know that the sine function has negative in third quadrant

 $sin^{-1} (\frac{-1}{2} ) = sin^{-1} ( sin (\pi +\frac{\pi }{6} )$

We have to use trigonometric formula

$sin^{-1} ( sin (x)) = x$

Step(ii):-

$sin^{-1} (\frac{-1}{2} ) = sin^{-1} ( sin (\pi +\frac{\pi }{6} ) = \pi +\frac{\pi }{6}$

                                                = $\frac{6\pi +\pi }{6} = \frac{7\pi }{6}$

Final answer:-

The exact value

  $sin^{-1} (\frac{-1}{2} ) = \frac{7\pi }{6}$