Final answer:
The cot t for the point (-√33/7, 4/7) is -√33/4, while the sin t for the point (-√33/7, -4/7) is -4/7.
Step-by-step explanation:
The student is asking for help in finding trigonometric values given coordinates on the unit circle. Specifically, they want to find the cotangent of an angle θ (cot θ) when the coordinates are (-√33/7, 4/7), and the sine of θ (sin θ) when the coordinates are (-√33/7, -4/7). To resolve this, we recognize that the given coordinates correspond to the points on the unit circle related to an angle θ, in standard position, where the x-coordinate corresponds to the cosine of θ and the y-coordinate corresponds to the sine of θ.
For the point (-√33/7, 4/7), cot θ is the ratio of the x-coordinate to the y-coordinate, cot θ = (-√33/7) / (4/7) = -√33/4. For the point (-√33/7, -4/7), sin θ is simply the y-coordinate, sin θ = -4/7.