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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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