Name the quadrant in which the angle θ lies.
- $\cos \theta > 0 , \quad \csc \theta < 0$

Question

Name the quadrant in which the angle θ lies.
-$\cos \theta > 0 , \quad \csc \theta < 0$
A) I
B) II
C) III
D) IV

Quizplus · Accepted Answer

The cosine function is positive in the first and fourth quadrants, while the cosecant function, which is the reciprocal of the sine function, is negative when the sine function is negative. Since the sine function is positive in the first and second quadrants and negative in the third and fourth quadrants, the conditions are satisfied only in the fourth quadrant where cosine is positive and sine (hence, cosecant) is negative.

Name the Quadrant in Which the Angle θ Lies cos⁡θ>0,csc⁡θ<0\cos \theta > 0 , \quad \csc \theta < 0cosθ>0,cscθ<0

Name the Quadrant in Which the Angle θ Lies $\cos \theta > 0 , \quad \csc \theta < 0$