Question

How do you calculate the `arcsin (-1/ sqrt 2)`?

Answer 1

Calculate `arcsin (-1/sqrt2)`

Ans: `(5pi)/4 and (7pi)/4`

Explanation:

Unit circle and trig table of special arcs -->
`sin x = - 1/sqrt2 = - sqrt2/2` --> `arc x = - pi/4`
Unit circle gives another arc x that has the same sine value:
`x = pi + pi/4 = 5pi/4.`
Ans: `x = (5pi)/4`, and `x = (7pi)/4` (or -pi/4)