Question

In which quadrant is θ located if sin θ is negative and sec θ is positive? I, II, III, IV?

Answer 1

Answer: Quadrant II.

Step-by-step explanation:

1. The sine is negative in quadrant III and quadrant IV. Then:

sinθ<0 (Quadrant III and quadrant IV).

2. Secant is equal to $\frac{1}{cos(\theta )}$ and the cosine is positive in quadrant I and quadrant IV:

cosθ>0 (Quadrant I and Quadrant IV)  

Secθ>0 (Quadrant I and Quadrant IV)

3. We look for a quadrant where the sine is negative and the cosine is positive. We know that the sine is negative in the IV quadrant and that the cosine and secant are positive in the IV quadrant.

Therefore the correct answer is the last one: Quadrant IV