Question

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

Answer 1

The exact value

`sin^(-1) ((-1)/(2) ) = (7\pi )/(6)` = 210°

Explanation:

Step(i):-

Given that the inverse trigonometry

`sin^(-1) ((-1)/(2) )`

We know that the sine function has negative in third quadrant

`sin^(-1) ((-1)/(2) ) = sin^(-1) ( sin (\pi +(\pi )/(6) )`

We have to use trigonometric formula

`sin^(-1) ( sin (x)) = x`

Step(ii):-

`sin^(-1) ((-1)/(2) ) = sin^(-1) ( sin (\pi +(\pi )/(6) ) = \pi +(\pi )/(6)`

=
`(6\pi +\pi )/(6) = (7\pi )/(6)`

Final answer:-

The exact value

`sin^(-1) ((-1)/(2) ) = (7\pi )/(6)`