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Next: Some Familiar Angles Up: Basic Trigonometry Previous: Definitions of Sine and

Angles in Different Quadrants

reference.epsThe above figure shows four possible positions of the angle tex2html_wrap_inline715 --one in each of the four quadrants. Another angle, tex2html_wrap_inline811 , is also marked. This is sometimes called the reference angle for tex2html_wrap_inline715 . In each case, tex2html_wrap_inline815 and tex2html_wrap_inline817 . Also, tex2html_wrap_inline819 , recalling that tex2html_wrap_inline821 . The choice of tex2html_wrap_inline823 depends upon the quadrant.

  1. Quadrant I
    1. tex2html_wrap_inline825 .
    2. tex2html_wrap_inline827 .
    3. tex2html_wrap_inline829 .
  2. Quadrant II
    1. tex2html_wrap_inline825 .
    2. tex2html_wrap_inline833 .
    3. tex2html_wrap_inline835 .
  3. Quadrant III
    1. tex2html_wrap_inline837 .
    2. tex2html_wrap_inline839 .
    3. tex2html_wrap_inline841 .
  4. Quadrant IV
    1. tex2html_wrap_inline837 .
    2. tex2html_wrap_inline827 .
    3. tex2html_wrap_inline835 .

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:

All three trig functions are positive in Quadrant I.
Only Sine is positive in Quadrant II; the others are negative.
Only Tangent is positive in Quadrant III; the others are negative.
Only Cosine is positive in Quadrant IV; the others are negative.

Carl Lee
Wed Apr 21 08:17:28 EDT 1999