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Sine and cosine theorem

The animation shows the geometric relationships of the sine and cosine theorem.

The red dot can be adjusted with the mouse.

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

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Description

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

The animation shows a right-angled triangle. The adjacent leg of the angle alpha is marked in blue, the opposite leg is red. Like the adjacent leg, the cosine curve is in blue, the sinusoid curve is red.

Like the adjacent leg, the cosine curve is also represented by blue. The sinusoid curve is red. The bent arc length of the angle is green.

The animation shows that the height of the opposing cathetus (leg) 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 (adjacent side) is also illustrated by a guide line. Because of the perspective, it is only possible to show the sinusoidal curve but not with the cosine curve.

Clicking inside the large rectangle will generate the formulas.

General information

Title:Sine and cosine theorem
Target group:
  • Teachers and lecturers
  • Independent learners
Platforms (primary):
  • Microsoft® Windows®
  • Microsoft® PowerPoint®
  • Apple® Macintosh®
Features
  • Resizable without the loss of visual clarity
  • No installation required
DocumentsLicensing Information

Tips

The lengths of the adjacent side (X) and the opposite side (Y) are also displayed as exact values in the input fields. These values cannot be changed via the input fields. Instead, only the angle alpha can be changed. To set an angle, you can employ the two rotary fields (degrees and radian measures) in the upper right side.

Further animations for PCs

Die Animation zeigt ein Dreieck, das interaktiv verndert 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 verndert werden kann. Die Ober- und Untersumme wird automatisch im Bereich des Integrals eingezeichnet.
Fundamentals of the integral calculus

Further animations for smartphones/tablets


Calculation of the outer circle of a triangle


Calculation of the inner circle of a triangle


Calculation of the center of gravity on a triangle


Geometric relationships on a square

Sources

Authoring tool: Adobe Animate

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