Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$\cos \left( \frac { \pi } { 4 } \right)$
A) $\frac { \sqrt { 2 } } { 2 }$
B) $\frac { \sqrt { 3 } } { 2 }$
C) $\frac { 1 } { 2 }$
D) $\sqrt { 2 }$

Question

Quizplus · Accepted Answer

The angle $\frac{\pi}{4}$ is one of the special angles in trigonometry where the values of sine, cosine, and tangent can be determined exactly. To see this, draw a 45-45-90 right triangle with hypotenuse 1, which has legs of length $\frac{1}{\sqrt{2}}$. By definition of cosine, $\cos(\frac{\pi}{4})$ is the adjacent side over the hypotenuse, which is $\frac{\sqrt{2}}{2}$.

Find the Exact Value of the Trigonometric Function cos⁡(π4)\cos \left( \frac { \pi } { 4 } \right)cos(4π​)

Find the Exact Value of the Trigonometric Function $\cos \left( \frac { \pi } { 4 } \right)$