How do you evaluate $sin^-1(-1/sqrt2)$ ?

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Answer 1 · 2016-07-14T17:05:48

$-pi/4$

Let $sin^-1(-1/sqrt2)=theta.$

Then, by defn. of $sin^-1, sintheta=-1/sqrt2$ , where, $theta in [-pi/2,pi/2]$

We have, $sin(-pi/4)=-1/sqrt2,$ & $-pi/4 in {-pi/2,pi/2]$ , $theta=-pi/4$

How do you evaluate sin^-1(-1/sqrt2)sin^-1(-1/sqrt2)?