Question

How do you solve and find the value of `sin^-1(1/sqrt2)`?

Answer 1

The angle = `pi/2 = 45^@`

Explanation:

`sin^-1(1/sqrt(2))` says, give me the angle that has a sin of `(1/sqrt(2)) = sqrt(2)/2`

Either from a trig circle or from a `45^@-45^@-90^@` triangle, that angle would be either `pi/4 = 45^@` or `(3 pi)/4 = 135^@`. However, the `arcsin` `(sin^-1)` function has a limited domain `[-1, 1]`and range `[-pi/2, pi/2] = [-90^@, 90^@]`. This means `(3 pi)/4 = 135^@` is not a valid answer.

You can see this from the graph `f(x) = arcsin(x) = sin^-1(x)`:
graph{arcsin(x) [-4.933, 4.932, -2.466, 2.467]}