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Sine, Cosine, and Tangent on a Circle


Date: 04/14/99 at 00:02:55
From: Willy Jongejan
Subject: The relation of sine, cosine, and tangent to a circle

This should be easy for you, but I'm stuck. Do you have any visuals 
of where the sine, cosine, and tangent are on a unit circle?

Thanks.


Date: 04/14/99 at 09:10:43
From: Doctor Rob
Subject: Re: The relation of sine, cosine, and tangent to a circle

                      Q  _..-----.._
                      .+'           `-.
                    ,' |\              `.
                  ,'   | \               `.
                 /     |  \1               \
                /      |   \                \
               . sin(x)|    \                .
               |       |     \ x      1      |
               +-------+------+--------------+ P
               |      R cos(x) \O            |
               .                \            .
                \                \          /|
                 \                \        / |
                  `.               \     ,'  |
                    `.              \  .'    |
                      `-._         _.-'      |
                          ''-----''   \      |tan(x)
                                       \     |
   x = <POQ,                      sec(x)\    |
   |sin(x)| = length(RQ),                \   |
   |cos(x)| = length(OR),                 \  |
   |tan(x)| = length(PS),                  \ |
   |sec(x)| = length(OS).                   \|
                                             o
                                              S

The signs of each are determined by which quadrant x falls in. If x is 
in the first quadrant, then all are positive. In this picture, x is in 
the second quadrant so the sine is positive and the rest negative.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Trigonometry

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