Evaluate the trigonometric function using its period as an aid.
$\cos \frac { 17 \pi } { 4 }$
A) $\cos \frac { 17 \pi } { 4 } = \sqrt { 2 }$
B) $\cos \frac { 17 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$
C) $\cos \frac { 17 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$
D) $\cos \frac { 17 \pi } { 4 } = - \sqrt { 2 }$
E) $\cos \frac { 17 \pi } { 4 } = \infty$

Question

Evaluate the trigonometric function using its period as an aid. 
$\cos \frac { 17 \pi } { 4 }$ 
A) $\cos \frac { 17 \pi } { 4 } = \sqrt { 2 }$
B) $\cos \frac { 17 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$
C) $\cos \frac { 17 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$
D) $\cos \frac { 17 \pi } { 4 } = - \sqrt { 2 }$
E) $\cos \frac { 17 \pi } { 4 } = \infty$

Quizplus · Accepted Answer

The period of the cosine function is $2\pi$. Therefore, $\cos \frac { 17 \pi } { 4 } = \cos \left( \frac { 16 \pi } { 4 } + \frac { \pi } { 4 } \right) = \cos \left( 4\pi + \frac { \pi } { 4 } \right) = \cos \frac { \pi } { 4 }$, which equals $\frac { \sqrt { 2 } } { 2 }$.

Evaluate the Trigonometric Function Using Its Period as an Aid cos⁡17π4\cos \frac { 17 \pi } { 4 }cos417π​

Evaluate the Trigonometric Function Using Its Period as an Aid $\cos \frac { 17 \pi } { 4 }$