Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$\sin \left( \frac { 5 \pi } { 3 } \right)$
A) $\frac { \sqrt { 2 } } { 2 }$
B) $\frac { \sqrt { 3 } } { 2 }$
C) $- \frac { \sqrt { 2 } } { 2 }$
D) $- \frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

$\sin \left( \frac { 5 \pi } { 3 } \right)$ corresponds to the sine of an angle in the fourth quadrant, where sine values are negative. The reference angle for $\frac { 5 \pi } { 3 }$ is $\frac { \pi } { 3 }$, whose sine is $\frac { \sqrt { 3 } } { 2 }$. Therefore, the answer is $- \frac { \sqrt { 3 } } { 2 }$.

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