You should memorize 

1. All trig ratios are positive in quadrant I

2. Only the SINE and its reciprocal, the COSECANT, are positive in quadrant II.
All others are negative.

3. Only the TANGENT and its reciprocal, the COTANGENT, are positive in 
quadrant III.  All others are negative.

4. Only the COSINE and its reciprocal, the SECANT, are positive in quadrant IV.
All others are negative.

Some students find it helpful to remember the sentence 

"ALL STUDENTS TAKE CALCULUS."

to remember  ALL, SINE, TANGENT, COSINE.  Then you know their reciprocals also
have the same signs.

The formulas for one trig ratio in terms of another trig ratio are different
for each quadrant. You were given quadrant IV. We begin by using ±, then we'll
figure out which sign we will use for quadrant IV.





Now we make sure that we pick the right sign.
In quadrant IV the sine and the secant have OPPOSITE signs.  So therefore, we
use the negative sign in front. So the answer for quadrant IV is




Edwin

"Hey, there is no any need to memorize the signs of trigonometry functions in four
quadrants."

Why not?  It's too much trouble to have to go through every time to think of
whether it's a positive over a positive, a positive over a negative, a negative
over a positive, or a negative over a negative.  Of course they can do that, but
on a test, they need to save time, not waste time going through the 4 sign facts
every time.

You may as well tell them there is no need to memorize the quadratic formula
because all they need do is complete the square.

Edwin