1. INTRODUCTION
In this tutorial, we will take a look at the three basic trigonometric
ratios, sine, cosine and tangent. If you find any errors or miscalculations
here, please inform me.
2. THE SINE RATIO
To calculate the sine of an angle, the opposite is divided by the hypotenuse.
The sine ratio is abbreviated as sin.
Formula: sin ang = opp / hyp (opposite is abbreviated as opp,
hypotenuse is abbreviated as hyp)
Example: sin 30 deg = 4 / 8 (the angle calculated is 30 degrees,
sin 30 deg = .5 the opposite is 4,
the hypotenuse is 8)
\
 \ the adjacent is of no importance
 \ 8 a is a right angle
4  \ hyp
opp  \
 \
 \
 a 30 \

adj (adjacent)
3. COSINE RATIO
To calculate the cosine of an angle, instead of dividing the opposite by the
hypotenuse, you divide the adjacent by the hypotenuse. Cosine is abbreviated
as cos.
Formula: cos ang = adj / hyp
Example: cos 60 deg = 3 / 6 (the angle calculated is 30 degrees,
cos 60 deg = .5 the adjacent is 3,
the hypotenuse is 6)
\
 \ 6 this time the opposite is of no importance
 \ hyp a is a right angle
opp  \
 \
 a 60 \

3
adj
4. THE TANGENT RATIO
The tangent of an angle is determined by dividing the opposite by the
adjacent. Tangent is abbreviated as tan.
Formula: tan ang = opp / adj
Example: tan 60 deg = 14 / 20 (the angle is 30 degrees,
tan 60 deg = .7 the opposite is 14,
the adjacent is 20)

14  in this situation, the hypotenuse is ignored
opp 
 / hyp
 /
 /
 /
 / 30

20
adj
5. RATIOS AS PART OF A CIRCLE
Here the same techniques are demonstrated on a full rotation, with triangles
cut out. This is a more realistic example using X/Y coordinates.
y

D  B
r  r (radius of the circle)
\  /
\  /
\  /
C obtuse \  / acute A
 x
E /  \ G
/  \
/  \
/  \
r  r
F  H
reflex  reflex
Try applying some of the techniques on this circle. Acute, obtuse and reflex
are the types of angles.

Copyright (C) 2000 Lionel Pinkhard. All Rights Reserved.

