In which quadrant does theta lie if the following statements are true? Secant theta > 0 and (cos theta)(tan theta)<0

Answer 1

Let's call the angle x instead of theta!

secant(x) > 0

secant(x) = 1/cos(x) > 0

If secant(x) is positive, cos(x) is also positive.

Positive cos(x). ==> Q1 or Q4

cos(x) * tan(x) < 0

cos(x) * sin(x)/cos(x) < 0

sin(x) < 0

Negative sin(x) ==> Q3 or Q4

ANSWER: The angle is in Q4