Can you name the quadrant in which the angle θ lies?

Question

1. sin θ >0, cos θ <0
2. sin θ < 0, tan θ < 0
3. cos θ > 0, tan θ > 0
4. cos θ > 0, cot θ < 0

Answer 1

This handy "CAST" diagram tells you which ratios are positive in each quadrant.

A = all ratios are positive in Q1

S = sinθ is positive in Q2 (the other ratios are negative)

T = tanθ is positive in Q3 (the other ratios are negative)

C = cosθ is positive in Q4 (the other ratios are negative)

Since cotθ is 1/tanθ, it would be positive or negative in the same quadrants as tanθ