If sin θ < 0 and cot θ > 0, name the quadrant in which the angle θ lies?
- 4th quadrant
- 3rd quadrant
- 2nd quadrant
- None of these
Explanation
Given:
sin θ < 0 (sine is negative)
cot θ > 0 (cotangent is positive)
Since cot θ = cos θ / sin θ, and cot θ > 0, we know that cos θ and sin θ must have the same sign (both positive or both negative).
Given sin θ < 0, cos θ must also be negative.
The quadrant where both sine and cosine are negative is the 3rd quadrant.
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