Final Answer:
The given conditions are satisfied in Quadrant III (option c).
Step-by-step explanation:
To determine in which quadrant sin < 0 and cot > 0, let's consider the signs of these trigonometric functions in each quadrant (option c).
In Quadrant I, all trigonometric functions are positive. In Quadrant II, sin is positive, but cot is negative. In Quadrant III, both sin and cot are negative, satisfying the given conditions. In Quadrant IV, sin is negative, but cot is positive.
Therefore, the correct quadrant is Quadrant III, where sin < 0 and cot > 0. This is the final answer.
Understanding the signs of trigonometric functions in each quadrant is essential for solving problems involving angles and their corresponding values. In this case, recognizing the characteristics of sine and cotangent functions in Quadrant III leads to the accurate identification of the quadrant that meets the specified criteria.