Question

Why is the value of arcsin(sin(5pi/4)) -pi/4 and not 5pi/4? Thank you. :)

Answer 1

The arcsin(x) FUNCTION is defined ONLY on [-pi/2,pi/2]. If you do not start in this range, you will be forced here by the arcsin(x) function.

Answer 2

How do you check if its in that range?

Answer 3

it is a number
the number is either between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) or it is not

Answer 4

since \(\frac{5\pi}{4}>\frac{\pi}{2}\) it is not in the range of arcsine
you have to pick the number between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) that works

Answer 5

I get that now! :) Thank you so much!!

Answer 6

in other words you want a number between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) where the sine will be the same as the sine of \(\frac{5\pi}{4}\)
it is easy to visualize, go right across the unit circle to get it

Answer 7

yw