How do you evaluate $arcsin (- 1)$ $arcsin(-1)$ without a calculator?

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Answer 1 · 2016-11-23T13:44:53

$arcsin (- 1) = - \frac{π}{2}$ $arcsin(-1)=-pi/2$

$arcsin x$ $arcsinx$ means the angle whose sine ratio is $x$ $x$ i.e. $θ$ $theta$ where $sin θ = x$ $sintheta=x$ .

Hence, $arcsin (- 1)$ $arcsin(-1)$ means the angle whose sine ratio is $- 1$ $-1$ .

As $sin (- \frac{π}{2}) = - 1$ $sin(-pi/2)=-1$

$arcsin (- 1) = - \frac{π}{2}$ $arcsin(-1)=-pi/2$

How do you evaluate arcsin(−1)arcsin(-1) without a calculator?