How do you find the exact value of $arcsin (-1/2)$ ?

Question

61769 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-09T03:36:32

$-pi/6$

Arcsin can be thought of as the ANGLE with the specified value of sin.

The range of $arcsin$ or $sin^-1$ is $pi/2$ to $-pi/2$ .

Arcsin of a positive value is found in QI or zero to $pi/2$ .
Arcsin of a negative value is found in QIV or zero to $-pi/2$

In this case, $arcsin(-1/2)$ is found in QIV. The angle with a sin of $-1/2$ in QIV is $-pi/6$ .

How do you find the exact value of arcsin (-1/2)arcsin (-1/2)?