(A) cos((7pi )/(4))= Using the Unit Circle . find the exact value of this trig function. -(1)/(2) (sqrt (2))/(2) (1)/(2) The correct answer is not listed -(sqrt (2))/(2)

To find the exact value of $\cos(\frac{7\pi}{4})$, we can use the unit circle.<br /><br />The unit circle is a circle with a radius of 1, and it is used to represent the values of trigonometric functions for different angles.<br /><br />In the unit circle, the angle $\frac{7\pi}{4}$ is located in the fourth quadrant. The cosine function represents the x-coordinate of a point on the unit circle.<br /><br />To find the exact value of $\cos(\frac{7\pi}{4})$, we can use the fact that the cosine function is positive in the fourth quadrant.<br /><br />The angle $\frac{7\pi}{4}$ is equivalent to $-\frac{\pi}{4}$, which is the same as $-\frac{\pi}{4} + 2\pi$. This angle is in the fourth quadrant, and the cosine function is positive in this quadrant.<br /><br />The reference angle for $\frac{7\pi}{4}$ is $\frac{\pi}{4}$, which is a common angle in the unit circle. The cosine of $\frac{\pi}{4}$ is $\frac{\sqrt{2}}{2}$.<br /><br />Therefore, the exact value of $\cos(\frac{7\pi}{4})$ is $\frac{\sqrt{2}}{2}$.<br /><br />So, the correct answer is $\frac{\sqrt{2}}{2}$.