How do you find inverse sin (-1/2)?
Using your calculator, press "shift" "
But since this is a negative, you cannot just write
Using the ASTC rule, you know that for
In Quadrant 3, from the ASTC rule, take
In Quadrant 4, from the ASTC rule, take
We use our knowledge of special angles together with the definition of inverse sine.
"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:
We know that
Therefore, the (principal) inverse sine of