Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.) $\cos \left(510^{\circ}\right)$

Step 1 ：Given the trigonometric function $\cos \left(510^{\circ}\right)$, we need to find its exact value.

Step 2 ：Since the cosine function has a period of 360 degrees, we can subtract 360 from 510 to get 150. So, $\cos(510^{\circ}) = \cos(150^{\circ})$.

Step 3 ：Next, we calculate the cosine of 150 degrees. We first convert the angle from degrees to radians, as the cosine function in most programming languages takes input in radians. The conversion is done using the formula: radians = degrees * $\pi$ / 180.

Step 4 ：Substituting 150 degrees into the formula, we get: angle_in_radians = 150 * $\pi$ / 180 = 2.6179938779914944.

Step 5 ：Finally, we calculate the cosine of the angle_in_radians. Using the cosine function, we get: cos_value = $\cos(2.6179938779914944) = -0.8660254037844387$.

Step 6 ：So, the exact value of the trigonometric function $\cos \left(510^{\circ}\right)$ is \(\boxed{-0.8660254037844387}\).