In the third quadrant, the values of `sin theta and cos theta` are :

Options

A. positive and negative respectively
B. negative and positive respectively
C. both positive
D. both negative

Answer

To solve the question regarding the values of `sin θ` and `cos θ` in the third quadrant, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quadrants**:
- The Cartesian plane is divided into four quadrants:
- **First Quadrant**: Both `sin θ` and `cos θ` are positive.
- **Second Quadrant**: `sin θ` is positive, `cos θ` is negative.
- **Third Quadrant**: Both `sin θ` and `cos θ` are negative.
- **Fourth Quadrant**: `sin θ` is negative, `cos θ` is positive.

2. **Identify the Third Quadrant**:
- In the third quadrant, the angles range from 180° to 270° (or from π to 3π/2 radians).
- Here, the sine and cosine functions take on negative values.

3. **Conclusion**:
- Therefore, in the third quadrant, both `sin θ` and `cos θ` are negative.

### Final Answer:
In the third quadrant, the values of `sin θ` and `cos θ` are both negative.