Question

Which of the following is true?

Sine is negative in Quadrant I.
Tangent is positive in Quadrant III.
Cosine is positive in Quadrant III.
Sine is negative in Quadrant II.

Answer 1

There isn't really a way to explain it unless you try out some test angle values or you understand their natural behavior.

Q1: sin(π/6)=+
Q2: sin(2π/3)=+
Q3: sin(7π/6)=-
Q4: sin(5π/3)=-

Do the same for cos and tan, and you'll find that eventually:
All sine, cos, and tan are POSITIVE in quadrant 1.
Sine is Postive in quadrant 2.
Tan is positive in quadrant 3.
Cos is positive in quadrant 4.

This holds true for their reciprocal functions too, csc, cot, and sec.

Use this info and answer accordingly.

Answer 2

You must be well versed with the unit circle:

Answer 3

Thank you so much for your help! :))))