Question

How do you find the exact values of `sin^-1(1/2)`?

Answer 1

`sin^-1(1/2)=pi/6`

Explanation:

Find `sin^-1(1/2)`

This problem is asking for the ANGLE with a sine of `1/2`.

The range of `sin^-1` or `arcsin` is between `pi/2` and `-pi/2`.

If you are finding `sin^-1` of a positive value, the answer will be between 0 and `pi/2`, or the first quadrant in the unit circle. Do NOT use the second quadrant angle with a sine of `1/2`, because it does not fall within the range of `sin^-1`.

Using the unit circle, the angle with a sine of `1/2` in the first quadrant is `pi/6`.