How do you find inverse sin (-1/2)?

2 Answers
Oct 10, 2015

#210°, 330°#

Explanation:

Using your calculator, press "shift" "#sin (1/2)#" and it will give you #30#. (Always ignore the negative when you are doing the inverse!)

But since this is a negative, you cannot just write #30°# as your final answer.

Using the ASTC rule, you know that for #sin# to be positive it has to be in Quadrant 1 and 2. But since this is a negative it has to be the complete opposite! So Quadrant 3 and 4 is where #sin# will be negative.

In Quadrant 3, from the ASTC rule, take #180°+prop# #rArr# #prop# being the answer you just got aka #30°#!

In Quadrant 4, from the ASTC rule, take #360°-prop# .

So,

#180°+30°=210°#
#360°-30°=330°#

Oct 10, 2015

We use our knowledge of special angles together with the definition of inverse sine.

Explanation:

"inverse sine" may refer to either a single values function (the principal value -- common in introductory courses) or to a "multivalued function".

Here is the definition for the principal value:

#y=arcsinx# if and only if #(-pi/2 <= y <= pi/2 bb" and " siny=x)#

We know that #sin(pi/6) = 1/2# and so, #sin(-pi/6) = -1/2#.

Therefore, the (principal) inverse sine of #-1/2# is #-pi/6#.