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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.

## Description

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.

## General

Title: Sine and cosine theorem Teachers and lecturersSelf-learners Microsoft® Windows®Microsoft® PowerPoint®Apple® Macintosh® Enlargeable without lossNo installation required License Information About the security of the Flash Player

## Tips

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.

Geometric relations on the triangle

Pythagorean theorem

Basis of the integral calculus

## Feedback

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