How do you evaluate $sin^-1(-sqrt2/2)$ without a calculator?

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Answer 1 · 2016-11-30T10:40:03

$sin^(-1)(-sqrt(2)/2) = -pi/4$

This is a known value for $sin(x)$ , you should remember that:

$sin(pi/4) = sqrt(2)/2$

and that:

$sin(-x) = -sin(x)$

Although many other angles have the same value for sine, namely:

$alpha = -pi/4+2kpi$
and
$alpha = -(3pi)/4 +2kpi$

conventionally $arcsin(x)$ is defined in the interval $[-pi/2,pi/2]$
so you pick the value:

$x=-pi/4$

How do you evaluate sin^-1(-sqrt2/2)sin^-1(-sqrt2/2) without a calculator?