I have the answers to the question, but I have no on how to get the answers.

Question

State the quadrant in which theta lies.

Cos X < 0 and Sin X > 0 (Answer is 2)
Tan X < 0 and Sin X < 0 (Answer is 4)
Cos X > 0 and Tan X > 0 (Answer is 1)
Cot X < 0 and Sec X < 0 (Answer is 3)

Answer 1

Q2 Q1
Q3 Q4

S.....A
T.....C

"All Students Take Calculus"

A = All things in Q1 are positive
S = Sine (and cosecant) are positive in Q2 [since it's above the x-axis]
T = Tangent (and cotangent) are positive in Q3 [since it's sin/cos and both sin and cos are negative in Q3]
C = Cosine (and secant) are positive in Q4 [since it's to the right of the y-axis]