Use periodic properties of the trigonometric functions to find the exact value of the expression.
-$\sin \frac { 17 \pi } { 3 }$
A) $- \frac { \sqrt { 3 } } { 2 }$
B) 2
C) $\frac { \sqrt { 3 } } { 2 }$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

$\sin \frac { 17 \pi } { 3 }$ simplifies to $\sin (5\pi + \frac { 2\pi } { 3 })$, which is equivalent to $\sin \frac { 2\pi } { 3 }$. Since $\sin \frac { 2\pi } { 3 } = \sin ( \pi - \frac { \pi } { 3 }) = \sin \frac { \pi } { 3 } = \frac { \sqrt { 3 } } { 2 }$, but in the second quadrant where sine is positive, the answer is $- \frac { \sqrt { 3 } } { 2 }$ due to the periodic nature of the sine function and the original angle being more than $2\pi$, indicating a negative sine value in the quadrant it lands.

Use Periodic Properties of the Trigonometric Functions to Find the Exact