Answer:
Explanation:
To find the exact value of cot(θ), we need to determine the ratio of the adjacent side to the opposite side of the right triangle formed by the given point (12, -5).
Let's label the coordinates of the point as follows: x = 12 and y = -5.
We can calculate the length of the adjacent side and the opposite side using the Pythagorean theorem:
Adjacent side (x-coordinate) = 12
Opposite side (y-coordinate) = -5
Now, we can determine the value of cot(θ) by taking the ratio of the adjacent side to the opposite side:
cot(θ) = adjacent side / opposite side
= x / y
Substituting the values, we get:
cot(θ) = 12 / -5
To simplify the expression, we can multiply the numerator and denominator by -1 to obtain a positive denominator:
cot(θ) = -12 / 5
Therefore, the exact value of cot(θ) in simplest radical form is -12/5.