Give the exact value of the expression.
-$$\csc \left( \sin ^ { - 1 } \frac { 18 } { 30 } \right)$$

Question

Quizplus · Accepted Answer

The expression $\csc \left( \sin ^ { - 1 } \frac { 18 } { 30 } \right)$ simplifies to the reciprocal of $\sin \left( \sin ^ { - 1 } \frac { 18 } { 30 } \right)$, which is $\frac { 30 } { 18 }$, because $\csc(\theta) = \frac{1}{\sin(\theta)}$. Simplifying $\frac { 18 } { 30 }$ gives $\frac { 3 } { 5 }$, and the reciprocal of that is $\frac { 5 } { 3 }$, which, when scaled back to the original numbers, is $\frac { 30 } { 18 }$.

Give the Exact Value of the Expression csc⁡(sin⁡−11830)\csc \left( \sin ^ { - 1 } \frac { 18 } { 30 } \right)csc(sin−13018​)

Give the Exact Value of the Expression $\csc \left( \sin ^ { - 1 } \frac { 18 } { 30 } \right)$