Question

arcsin(sin(9pi/4))

Answer 1

Sine and Arcsine are inverse operations of one another. So they essentially "undo" each other. Which would lead you to believe that \(\large \arcsin(\sin(\dfrac{9\pi}{4}))=\dfrac{9\pi}{4}\).

The problem is, the arcsine, in order to be a function, needs it's domain restricted from, \(\large -\pi/2\) to \(\large \pi/2\). So.....

Answer 2

This is our angle, 9pi/4. Does it have a reference angle within the domain that we setup?

Answer 3

We're looking for an angle in the first or fourth quadrant that lands in the same spot.