5th grade
Natural numbers
Basic arithmetic operations
Calculation laws and advantages
Geometry

6th grade
Divisibility of numbers
Factions
Decimal fractions
Angles and angle measures

7th grade
Assignment and rule of three
Calculation of percentage
Rational numbers
Equation and inequation
Probability calculus

8th grade
Function and assignment
Triangles
Quadrangles
Calculation of surfaces
Transformation of terms
Probability calculus

9th grade
The root
Record set of the pythagoras

10th grade
Circle calculation
The cone
Power calculation
Power laws
Exponential function
Logarithm
Trigonometry
Probability calculus

 

Sine
The sine function

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The sine function in the unit circle

 

In the unit circle, the angle alpha is assigned to the y-coordinate of the point of intersection S on the circle as sine. This means that in the unit circle the cosine of alpha is equal to the sine of alpha.

 

Cognitions that are recognised on the base of a unit circle

sin (90° + x) = sin (90° - x)

sin (180° + x) = - sin (180° - x)

sin a = - sin (360° - a)

sin a = sin (360° + a)


 

Sine function in the coordinate system

The sine curve is an odd function, that is symetrical to the point 0 (0;0) and repeats itself after 3600 (periodically).

 

Special values that are in the sine funtion in the unit circle and in the coordinate system

30°

45°

60°

90°

120°

135°

150°

180°

0

1

0

 

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Copyright © 2005 Christian Franzki - Emkacom Group
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02/09/07