What is #arcsin 0#?

1 Answer
Jul 2, 2015

#arcsin 0 = 0#

Explanation:

#arcsinx# is a #theta# with #theta# between #-pi/2# and #pi/2# (between #-90^@# and #90^@#) with #sin theta =x#

So, #arc sin 0# is an number (an angle) in the correct range, with #sin theta =0#

The angles with sine = 0 are co-terminal with #0# or with #pi# (in degrees, with #180^@#)

The only such angle between #-pi/2# and #pi/2# is the angle #theta = 0#.

So #arcsin 0 =0# (Either the number #0# or the angle measuring #0# radians or #0^@# depending on the units of the application.)