Question

How do you find the general solutions for `sin x = -sqrt2/2`?

Answer 1

Solve `sin x = -(sqrt2)/2`

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

Explanation:

Trig table and trig unit circle give--> `sin x = -(sqrt2/2)` -->
`x = -pi/4`, or `(7pi)/4`
and `x = - (3pi)/4`, or `(5pi)/4`

General solutions: `x = (5pi)/4 + 2kpi` and `x = (7pi)/4 + 2kpi`