Question

Find the exact value of sin-1(-0.5).

Answer 1

Answer:
`(-\pi)/(6)`

Explanation:

To find : The exact value of
`\sin^(-1)(-0.5)` .

We know that
`\sin^(-1)((1)/(2))=(\pi)/(6)`.

The range of
`\sin^(-1)(x)` is between
`(-\pi)/(2)\text{ and }(\pi)/(2)`

Let
`t=\sin^(-1)(-0.5)`

`\sin t=-0.5=-\sin((\pi)/(6))=\sin((-\pi)/(6))\ [\text{Since }}\sin(-x)=-\sin x]`

`\sin((-\pi)/(6))=0.5`

Hence, the principal value of
`\sin^(-1)(-0.5)=(-\pi)/(6)`

Answer 2

we are asked to evaluate the expression sin-1(-0.5). The answer is an angle with units of degrees or radians. In this case, we use a calculator to evaluate the expression. The answer is -30 degrees or negative pi/6. The angle is valid in the third and fourth quadrants