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

Cotangent is negative when sine and cosine have opposite signs, which occurs in Quadrants II and IV. Secant, which is the reciprocal of cosine, is positive when cosine is positive, which happens in Quadrants I and IV. Therefore, the only quadrant where both conditions are satisfied is 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 $\cot ( \theta ) < 0$