Question

Evaluate: csc[2sin^-1(-3/5)] Please help!!

Answer 1

Do you just multiply that by 2??

Answer 2

So 2(-5/3) ??

Answer 3

Or you could do it without knowing what the exact value of arcsin(3/5) is...

Let y=arcsin(-3/5).

So sin(y)=-3/5

(this came from arcsin so let's keep in mind we are looking at the 4th quadrant this is where cos is positive and sin is negative)

So draw a right triangle for sin(y)=-3/5 in the 4th quadrant (where the central angle is y)

Find the adjacent side of that triangle because you will need it later to evaluate csc(2y)

Recall that csc and sin are recipocals so you could write
\[\csc(2y)=\frac{1}{\sin(2y)}=\frac{1}{2 \sin(y)\cos(y)}\]
You should be able to answer this now.