The Computer Graphics Companion Online Edition
Damian Scattergood 1999-2001
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The Computer Graphics Companion Online Edition Damian Scattergood 1999-2001 |
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TRIGONOMETRY |
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PI - p |
p being an irrational number.
where p = 3.1415926535897....
The current value of PI has been calculated to over 100,000 decimal places and
has proved to be endless.
· Calculation of PI.
PI can be calculated using an approximation of
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RADIAN MEASURE |
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Definition: The Angle subtended at the centre of a circle by an arc equal in length to the radius has a measure of 1 radian. By definition:
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PYTHAGORAS'S THEOREM |
Pythagoras's Theorem states that the square of the Hypotenuse (AB)
is equal to the sum of the
squares of the other two sides, (AC) and (BC).
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For a given right angle triangle
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TRIANGLE FORMULAS - 2D |
Hypotenuse = Opposite / SIN (Angle) = Adjacent / COS (Angle)
Adjacent = Hyponetuse * COS (Angle) = Opposite / TAN (Angle)
Opposite = Hypotenuse * SIN (Angle) = Adjacent * TAN (Angle)
SIN (Angle) = Opposite / Hyponetuse
COS (Angle) = Adjacent / Hypotenuse
TAN (Angle) = Opposite / Adjacent
COT (Angle) = Adjacent / Opposite
SEC (Angle) = Hypotenuse / Adjacent
CSC (Angle) = Hypotenuse / Opposite
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TRIANGLE FORMULAS - 3D |
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NOTES |
Signs:=
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Angle A |
sin A | cos A | tan A | cot A | sec A | csc A |
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0° |
0 |
1 |
0 |
± ¥ |
1 |
± ¥ |
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90° |
1 |
0 |
± ¥ |
0 |
± ¥ |
1 |
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180° |
0 |
-1 |
0 |
± ¥ |
-1 |
± ¥ |
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270° |
-1 |
0 |
± ¥ |
0 |
± ¥ |
-1 |
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Angle A |
sin A | cos A | tan A | cot A | sec A | csc A |
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30° |
½ |
½Ö 3 |
1/3Ö 3 |
Ö 3 |
2/3Ö 3 |
2 |
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45° |
½Ö 2 |
½Ö 2 |
1 |
1 |
Ö 2 |
Ö 2 |
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60° |
½Ö 3 |
½ |
Ö 3 |
1/3Ö 3 |
2 |
2/3Ö 3 |
ADDITION FORMULAS.
sin (a+b) = sin a * cosb+cos a*sin b
cos (a+b) = cos a * cos b- sin a*sin b
tan (a+b) = tan a + tan b
1-tan a * tan b
SUBTRACTION FORMULAS.
sin (a-b) = sin A * Cos B - Cos A * Sin B
cos (a-b) = Cos A * Cos B + Sin A * Sin B
tan (a-b) = tan A - Tan B
1 + Tan A * Tan B
Double Angle Formulas:
Sin 2A = 2 Sin A * Cos A
Cos 2A= Cos^2A - Sin ^2A = 1-2Sin ^2A = 2Cos^2A -1
Tan 2A = 2TanA
1-Tan^2A
PRODUCTS
SUM AND DIFFERENCE
