calculus help needed

Question

example: sin-1(-1/2)
how do you figure this out?

The sin^-1 means the arcSin, or the angle whose sine is ...

so sin^-1(1/2) is the angle whose sine is -.5, which is -30 degrees.

In your calculator, put in -.5, then press INV sin.

so as my answer do i put pi/6?

That is the answer in radians. It should be negative. There is an angle in the third quadrant that yields a sine of -1/2 also.