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

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Answer 1 · 2015-08-19T04:06:24

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

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

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 $x = (7pi)/4 + 2kpi$

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