Dear student,

Defining trigonometric signs are very easy.
In first quadrant all the trigonometric signs are positive.
In second quadrant only sin and cosec are positive and other are negative. In third quadrant only tan and cot are posiive and other are negative.
And, in fourth quadrant, only cos and sec are positive and other are negative.

For remembering the sign conventions I personally use the trick as - All Silver Tea Cups.

That Means:-

A for all, means all the trigonometric terms are positive.
S for sin and it's reciprocal are positive.
T for tan and it's reciprocal are positive.
C for cos and it's reciprocal are positive.