To determine the quadrant in which the angle 8 is located, we need to analyze the signs of the trigonometric functions provided.
1. The cosine function, cos(θ), is positive in the first and fourth quadrants.
2. The cotangent function, cot(θ), is the ratio of cosine to sine (cot(θ) = cos(θ)/sin(θ)). Cotangent is negative when cosine and sine have different signs. This occurs in the second and fourth quadrants, as in these quadrants, one of the values is positive and the other is negative.
Now, combining these two pieces of information:
- Since cos(8) is positive, we can only consider the first and fourth quadrants.
- Since cot(8) is negative, we can only consider the second and fourth quadrants.
The only quadrant that meets both criteria—where cosine is positive and cotangent is negative—is the fourth quadrant.