If $\theta$ is an angle in standard position and its terminal side passes through the point ( $12,-35$ ), find the exact value of $\cos \theta$ in simplest radical form.

Step 1 ：Given a point (12, -35) that the terminal side of the angle passes through.

Step 2 ：The cosine of an angle in standard position is given by the x-coordinate of the point on the unit circle that the terminal side of the angle passes through.

Step 3 ：However, the point (12, -35) is not on the unit circle. To find the x-coordinate of the corresponding point on the unit circle, we need to normalize the given point by dividing each of its coordinates by the distance from the origin to the point.

Step 4 ：The distance from the origin to the point (12, -35) is given by the Pythagorean theorem as \(\sqrt{12^2 + (-35)^2}\).

Step 5 ：Calculate the distance, which is 37.0.

Step 6 ：Normalize the x-coordinate by dividing it by the distance, which gives 0.32432432432432434.

Step 7 ：This is the cosine of the angle in standard position. However, the question asks for the exact value in simplest radical form.

Step 8 ：To convert this decimal to a radical, we need to recognize that it is the decimal approximation of the fraction 12/37.

Step 9 ：Therefore, the exact value of \(\cos \theta\) in simplest radical form is 12/37.

Step 10 ：Final Answer: \(\boxed{\frac{12}{37}}\)