Angles in Different Quadrants

reference.epsThe above figure shows four possible positions of the angle --one in each of the four quadrants. Another angle, , is also marked. This is sometimes called the reference angle for . In each case, and . Also, , recalling that . The choice of depends upon the quadrant.

1. Quadrant I
   1. .
   2. .
   3. .
2. Quadrant II
   1. .
   2. .
   3. .
3. Quadrant III
   1. .
   2. .
   3. .
4. Quadrant IV
   1. .
   2. .
   3. .

One mnemonic device to remember the signs of the trig functions sine, cosine and tangent (sine/cosine) in the four quadrants is A Smart Trig Class:

A

All three trig functions are positive in Quadrant I.

S

Only Sine is positive in Quadrant II; the others are negative.

T

Only Tangent is positive in Quadrant III; the others are negative.

C

Only Cosine is positive in Quadrant IV; the others are negative.