To determine the quadrant in which the angle of 8 degrees lies based on the values of cosine and cotangent, we need to understand the signs of these trigonometric functions in different quadrants.
1. **Cosine (cos)**: The cosine function is positive in the first quadrant and the fourth quadrant. This means that if extit{cos(8)} is positive, then the angle could be in either of these two quadrants.
2. **Cotangent (cot)**: Cotangent is defined as the ratio of cosine to sine, i.e., cot(θ) = cos(θ) / sin(θ). The cotangent function is positive in the first quadrant and the third quadrant, and it is negative in the second quadrant and the fourth quadrant.
Now, since we know that cos(8°) is positive and cot(8°) is negative, we evaluate the quadrants:
- In the first quadrant: cos is positive and cot is positive.
- In the second quadrant: cos is negative and cot is negative.
- In the third quadrant: cos is negative, cot is positive.
- In the fourth quadrant: cos is positive, cot is negative.
From this analysis, we can observe that the only quadrant where cosine is positive and cotangent is negative is the fourth quadrant.
Therefore, the angle 8 degrees is located in the fourth quadrant.