Evaluate the trigonometric function using its period as an aid. $\sin \frac { 3 \pi } { 4 }$
A) $\sin \frac { 3 \pi } { 4 } = \infty$
B) $\sin \frac { 3 \pi } { 4 } = - \sqrt { 2 }$
C) $\sin \frac { 3 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$
D) $\sin \frac { 3 \pi } { 4 } = \sqrt { 2 }$
E) $\sin \frac { 3 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$

Question

Evaluate the trigonometric function using its period as an aid.   $\sin \frac { 3 \pi } { 4 }$  
A) $\sin \frac { 3 \pi } { 4 } = \infty$
B) $\sin \frac { 3 \pi } { 4 } = - \sqrt { 2 }$
C) $\sin \frac { 3 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$
D) $\sin \frac { 3 \pi } { 4 } = \sqrt { 2 }$
E) $\sin \frac { 3 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$

Quizplus · Accepted Answer

The value of $\sin \frac { 3 \pi } { 4 }$ is positive and equals $\frac { \sqrt { 2 } } { 2 }$ because it is in the second quadrant where sine values are positive, and it corresponds to a 45-degree angle in standard position, whose sine is $\frac { \sqrt { 2 } } { 2 }$.

Evaluate the Trigonometric Function Using Its Period as an Aid sin⁡3π4\sin \frac { 3 \pi } { 4 }sin43π​

Evaluate the Trigonometric Function Using Its Period as an Aid $\sin \frac { 3 \pi } { 4 }$