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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

mertsj · Answer

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