precal
posted by Anonymous on .
Determine the quadrant in which theta lies:
sec theta>0 and cot theta<0

sec theta is positive where cos theta is positive. That would be the first and fourth quadrants. Cot theta is negative where tan theta is negative, and that would be in the second and fourth quadrants. The only quadrant that satifies both criteria is the fourth.

why is sec theta positive where cos theta is positive?

because sec theta = 1/cos theta.
Both functions have the same sign