Final answer:
To solve the expression cot(-5π), we use the unit circle method and find that the cotangent is undefined (or infinite).
Step-by-step explanation:
The unit circle is a helpful tool for evaluating trigonometric functions. To solve the expression cot(-5π) using the unit circle method, we need to find the value of the cotangent function at angle -5π radians.
On the unit circle, the cotangent of an angle is equal to the cosine divided by the sine. Since the cosine and sine values repeat after a full cycle (2π radians), we can look for the reference angle in the first quadrant that has the same cosine and sine values as -5π.
Since the cosine and sine values for -5π are the same as those for π, we can use the values from the unit circle to find the answer. In the first quadrant, the cosine is 1 and the sine is 0, so the cotangent is 1/0, which is undefined (or infinite).