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Sine and cosine theorem

The animation displays the geometric relationships of the sine and cosine theorem graphically.

The red dot can be moved interactively with the mouse.

The animation was developed as a offline application for Windows and Macintosh systems and for integration into Microsoft PowerPoint slides. The online version presented here serves as a preview. The exe or app file can be downloaded free of charge in the member area.

Full screen


The downloaded file can be included in PowerPoint.


To change the shape of the triangle, simply move the red dot. The marking points on the two curves are adjusted automatically.

The animation shows a right-angled triangle. The adjacent leg of the angle alpha is represented in the color blue, the opposite leg correspondingly in the color red. Like the adjacent leg, the cosine curve is in the color blue, the sinusoid curve to the color red. The bent arc is the right angle for the angle.

Like the adjacent leg, the cosine curve is also represented in the color blue, the sinusoid curve corresponding to the color red. The bent arc length of the angle is marked in green.

The animation shows that the height of the opposing catheters in the unit circle is identical to the sine value. The length of the adjacent leg is accordingly identical to the cosine value. The relationship between sinus curve and length of the ankathete is also illustrated by an auxiliary line. Because of the perspective, this is only possible with the sinusoidal curve but not with the cosine curve.

After clicking inside the large rectangle, this is reduced and the formulas appear.


Title:Sine and cosine theorem
Target group:
  • Teachers and lecturers
  • Self-learners
Platforms (primary):
  • Microsoft® Windows®
  • Microsoft® PowerPoint®
  • Apple® Macintosh®
  • Enlargeable without loss
  • No installation required
DocumentsLicense Information
About the security of the Flash Player


The lengths of the anchor chain (X) and the countercat (Y) are also displayed as exact values in the input fields. These values can not be changed via the input fields. Instead, only the angle alpha can be changed. To set an exact angle, you can also use the two rotary fields (degrees and radians) in the upper right corner.

Advanced animations for PCs

Die Animation zeigt ein Dreieck, das interaktiv verändert werden kann.
Geometric relations on the triangle

Die Animationn zeigt ein rechtwickliges Dreieck. Ein Eckpunkt kann verschoben werden. Die Quadrate, die aus den drei Seiten gebildet werden, passen sich automatisch an.
Pythagorean theorem

Die Animation zeigt eine Kurve, deren Form mit der Maus verändert werden kann. Die Ober- und Untersumme wird automatisch im Bereich des Integrals eingezeichnet.
Basis of the integral calculus

Further animations for smartphones / tablets

Calculation of the outer circle at the triangle

Calculation of the inner circle at the triangle

Calculation of the center of gravity of a triangle

Geometric relationships at the quadrangle


Authoring tool: Adobe Animate

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