Which quadrant (in unit circle) does theta lie, if sin theta < 0 and sec theta > 0

sin theta < 0 in quadrants 3 and 4

sec theta > 0 in quadrants 1 and 4

sin theta < 0 and sec theta > 0 = intersection of {3,4} and {1,4}

Quadrant 4.

My money is on quadrant 4. GO QUADRANT 4!

Which quadrant (in unit circle) does theta lie, if sin theta < 0 and sec theta > 0?

In the fourth Quadrant...the cosine is positive, the sine is negative...

1st Q --- all positive

2nd Q -- sine positive (and its reciprocal)

3rd Q -- tangent positive

4th Q -- cosine positive

read your textbook...