Final answer:
The cosine function for angle theta is -√2/2, and the cotangent function for angle theta is -1.
Step-by-step explanation:
The cosine function for angle theta can be found by taking the x-coordinate of the point on the unit circle. In this case, the x-coordinate is -√2/2. Therefore, the cosine of angle theta is -√2/2.
To find the cotangent function for angle theta, we divide the x-coordinate by the y-coordinate of the point on the unit circle. In this case, the y-coordinate is √2/2. Therefore, the cotangent of angle theta is (-√2/2)/(√2/2), which simplifies to -1.