Question

Let Ø be an angle in standard position. What quadrant does angle Ø lie for the given conditions?

A) sec Ø > 0 and cot Ø < 0
B) cos Ø > 0 and sin Ø < 0
C) tan Ø > 0 and cot Ø > 0
D) sin Ø > 0 and cos Ø < 0

Answer 1

The angle Ø lies in Quadrant II when sin Ø > 0 and cos Ø < 0.

Step-by-step explanation:

To determine the quadrant in which an angle Ø lies based on given conditions, we need to consider the signs of the trigonometric ratios involved. Let's analyze each option:

A) sec Ø > 0 and cot Ø < 0: Based on the signs of sec Ø and cot Ø, we can determine that Ø lies in Quadrant II.

B) cos Ø > 0 and sin Ø < 0: With cos Ø > 0 and sin Ø < 0, Ø lies in Quadrant IV.

C) tan Ø > 0 and cot Ø > 0: Since both tan Ø and cot Ø are positive, Ø lies in Quadrant I.

D) sin Ø > 0 and cos Ø < 0: With sin Ø > 0 and cos Ø < 0, Ø lies in Quadrant II.

Therefore, the correct answer is D) sin Ø > 0 and cos Ø < 0, indicating that Ø lies in Quadrant II.