Evaluate the trigonometric function using its period as an aid. $\sin \left( \frac { 11 \pi } { 6 } \right)$
A) $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { 1 } { 2 }$
B) $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { \sqrt { 2 } } { 2 }$
C) $\sin \left( \frac { 11 \pi } { 6 } \right) = \infty$
D) $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { 1 } { 2 }$
E) $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { \sqrt { 2 } } { 2 }$

Question

Evaluate the trigonometric function using its period as an aid.​ $\sin \left( \frac { 11 \pi } { 6 } \right)$ ​
A) $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { 1 } { 2 }$
B) $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { \sqrt { 2 } } { 2 }$
C) $\sin \left( \frac { 11 \pi } { 6 } \right) = \infty$
D) $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { 1 } { 2 }$
E) $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { \sqrt { 2 } } { 2 }$

Quizplus · Accepted Answer

$\sin \left( \frac { 11 \pi } { 6 } \right)$ corresponds to the sine of an angle in the fourth quadrant, where sine values are negative. The equivalent angle in the first quadrant is $\frac{\pi}{6}$, for which $\sin(\frac{\pi}{6}) = \frac{1}{2}$. Therefore, in the fourth quadrant, it becomes $-\frac{1}{2}$.

Evaluate the Trigonometric Function Using Its Period as an Aid sin⁡(11π6)\sin \left( \frac { 11 \pi } { 6 } \right)sin(611π​)

Evaluate the Trigonometric Function Using Its Period as an Aid $\sin \left( \frac { 11 \pi } { 6 } \right)$