Visualization of trigonometric ratios

Trigonometry studies the relationship between angles and lengths (in right-angle triangles to start with, then in any triangle as well as in more complex geometric shapes).

The geometric transformations which preserve the angles (they are called similarities in Euclidian geometry) can change the lengths, but they preserve the ratio of lengths (or distances).

The most basic case is when you have similar triangles, characterized by equal angles. If two triangles are right-angle, if they have a second angle equal between them, they are similar. The ratio of length is preserved, which means (and this is an equivalent condition) that the sides of one are proportional to the sides of the others.

This video helps to visualize the trigonometric ratios in a unit circle.

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