Question

How do you simplify `sin^(-1)(- 1/2)`?

Answer 1

`sin^-1(-1/2)=-pi/6`.

Explanation:

Let `sin^-1(-1/2)=theta.`:. By defn. of `sin^-1` fun., we have,

`sintheta=-1/2, and, theta in [-pi/2,pi/2]`.

Recall that, `sin(pi/6)=1/2, so, sin(-pi/6)=-sin(pi/6)=-1/2`

Thus, `sin(-pi/6)=-1/2, &, -pi/6 in [-pi/2,pi/2]`.

`:. sin^-1(-1/2)=-pi/6`.