Identify the quadrant for the angle $\theta$ satisfying the following conditions.
- $\cos \theta > 0 \text { and } \csc \theta < 0$

Question

Identify the quadrant for the angle $\theta$ satisfying the following conditions.
-$\cos \theta > 0 \text { and } \csc \theta < 0$
A) Quadrant I
B) Quadrant II
C) Quadrant IV
D) Quadrant III

Quizplus · Accepted Answer

The cosine function is positive in Quadrants I and IV, while the cosecant function, which is the reciprocal of the sine function, is negative when the sine function is negative. Since sine is positive in Quadrants I and II, it is negative in Quadrants III and IV. Therefore, for both conditions ($\cos \theta > 0$ and $\csc \theta < 0$) to be satisfied, $\theta$ must be in Quadrant IV.

Identify the Quadrant for the Angle θ\thetaθ Satisfying the Following Conditions cos⁡θ>0 and csc⁡θ<0\cos \theta > 0 \text { and } \csc \theta < 0cosθ>0 and cscθ<0

Identify the Quadrant for the Angle $\theta$ Satisfying the Following Conditions $\cos \theta > 0 \text { and } \csc \theta < 0$