State the quadrant in which $\theta$ lies. $\cot ( \theta ) 0$ A) Quadrant III B) Quadrant I C) Quadrant IV D) Quadrant II E) Quadrant I or Quadrant III

Question

State the quadrant in which $\theta$ lies. $\cot ( \theta ) < 0$ and $\sec ( \theta ) > 0$
A) Quadrant III
B) Quadrant I
C) Quadrant IV
D) Quadrant II
E) Quadrant I or Quadrant III

Quizplus · Accepted Answer

Since $\sec( heta) > 0$, we know that $\cos( heta) > 0$, which eliminates quadrants II and III. Since $\cot( heta) < 0$, we know that $\frac{\cos( heta)}{\sin( heta)} < 0$. This happens when $\cos( heta) < 0$ and $\sin( heta) > 0$, which is true in quadrant IV. Therefore, the answer is (C) Quadrant IV.

State the Quadrant in Which θ\thetaθ Lies cot⁡(θ)<0\cot ( \theta ) < 0cot(θ)<0

State the Quadrant in Which $\theta$ Lies $\cot ( \theta ) < 0$