How do you find the exact value of $sin^-1(-1)$ ?

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Answer 1 · 2016-09-10T04:58:20

$-pi/2$

The range of arcsin is defined as between $-pi/2$ radians and $pi/2$ radians.

arcsin(x) is the one angle within this range whose sine is x

The one angle between $-pi/2$ and $pi/2$ with a $sin(x)=-1$ is $x = -pi/2$

On the unit circle, a sin of -1 falls on the negative x axis,
which is at $-pi/2$

How do you find the exact value of sin^-1(-1)sin^-1(-1)?