Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$\csc \left( \frac { \pi } { 3 } \right)$
A) $\frac { \sqrt { 3 } } { 2 }$
B) 2
C) $\sqrt { 2 }$
D) $\frac { 2 \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The cosecant function is the reciprocal of the sine function. $\csc \left( \frac { \pi } { 3 } \right) = \frac{1}{\sin \left( \frac { \pi } { 3 } \right)}$. Since $\sin \left( \frac { \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 }$, the reciprocal is $\frac { 2 \sqrt { 3 } } { 3 }$.

Find the Exact Value of the Trigonometric Function csc⁡(π3)\csc \left( \frac { \pi } { 3 } \right)csc(3π​)

Find the Exact Value of the Trigonometric Function $\csc \left( \frac { \pi } { 3 } \right)$