# If cos >0 and sin <0 what quadrant is it in?

##### 2 Answers

Consider the rule

Both of these rules indicate in which quadrant the trigonometric function is positive. In all quadrants except the first, only 1 out of the three trigonometric functions are positive; the other two are negative.

Quadrant 1: All are positive

Quadrant 2: Sine is positive

Quadrant 3: Tangent is positive

Quadrant 4: Cosine is positive

The acronym and the expression mentioned above are meant to facilitate your ability to remember these. Beware, though that C-A-S-T starts in the 4th quadrant and then goes to the 1st, 2nd and finally the 3rd, while "All Slow Turtles Crawl# goes from 1st to 4th.

Now, back to the problem at hand.

If cosine is positive, then we are already limited to 2 quadrants: IV and I. However, in quadrant I, all the functions are positive, and the problem says that sin is negative in this case. This leaves us one option: quadrant IV.

Hopefully this helps!

#### Explanation:

Cosine correlates with values of

Values of

Cosine is positive in the same quadrants.

Sine correlates with values of

Values of

Sine is negative in the same quadrants.

The only quadrant where

An example of an angle in

#cos((7pi)/4)=sqrt2/2>0#

#sin((7pi)/4)=-sqrt2/2<0#