In which quadrant must the terminal side of θ lie if sin θ and cot θ are to have the different sign?
A)IV
B)II and III
C)I and IV
D)I and II
E)III and IV

Question

In which quadrant must the terminal side of θ  lie if sin θ  and cot  θ  are to have the different sign? ​
A)IV
B)II and III
C)I and IV
D)I and II
E)III and IV

Quizplus · Accepted Answer

Recall that the sine function is positive in Quadrants I and II, and negative in Quadrants III and IV. On the other hand, the cotangent function is positive in Quadrants I and IV, and negative in Quadrants II and III.

Therefore, if sin θ and cot θ have different signs, then θ must lie in Quadrants II and III, which is the only region where sine is positive and cotangent is negative.

In Which Quadrant Must the Terminal Side of θ Lie