## anonymous 4 years ago Help with finding principal value. I've memorized the unit circle , but my teacher was very vague over principal values.

1. anonymous

i dont get how $\sin^{-1} (-\sqrt{2}/2) is -\pi/4$

2. anonymous

because $\sin(-\frac{\pi}{4})=-\frac{\sqrt{2}}{2}$

3. anonymous

you are looking for the angle (number) in the interval $[-\frac{\pi}{2},\frac{\pi}{2}]$ where the sine is your number

4. anonymous

there are an infinite number of numbers whose sine is anything between -1 and 1 because it is periodic, but only one in the above mentioned interval

5. anonymous

So it sin inverse would only be in the first quadrant of the unit circle?

6. Mertsj

No. It could also be in the 4th quadrant. All values for sin^-1 are, by definition, in quadrants I or IV