Question

How do you evaluate `arcsin(sqrt2/2)` without a calculator?

Answer 1

`pi/4 + 2kpi`
`(3pi)/4 + 2kpi`

Explanation:

Use trig table and unit circle:
`sin x = sqrt2/2` --> trig table gives --> arc `x = pi/4`.
Unit circle gives another arc x that has the same sin value:
`x = (pi - pi/4) = (3pi)/4`.
General answers:
`x = pi/4 + 2kpi`
`x = (3pi)4 + 2kpi`