What is sin^−1(-√3 / 2)?

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Answer 1 · 2018-02-25T09:55:53

$sin^-1(sqrt3/2) = 240° or 300°$

A right-angled triangle with angles of $60°and 30°$ has sides in the ratio $1 : sqrt3 : 2$

The core angle of $sqrt3/2$ is $60°$

However, the negative sign indicates that we are working with an angle in the $3rd or 4 th$ quadrants.

In the $3rd$ quadrant: $theta = 180° + 60° = 240°$

In the $4 th$ quadrant: $theta = 360°-60° =300°$

$sin^-1(sqrt3/2) = 240° or 300°$

Check using a calculator.

$sin 240° = -0.866$
$sin 300° = -0.866$

$-sqrt3/2 = -0.866$