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A helix casts two shadows: sine and cosine. · XDL

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A helix casts two shadows: sine and cosine.

A helix casts two shadows: sine and cosine.

@Math Pulse

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A helix casts two shadows: sine and cosine.

Sine and cosine are the same wave seen from a different perspective.

How to draw shadows at different angles!

Euler's formula eⁱθ = cos θ + i sin θ encodes rotation on the unit circle. An extra axis for the parameter θ converts the path into a helix of constant radius. Looking down the axis recovers the circle. The sine and cosine waves appear as the two orthogonal shadows of that

Simple shadow creation

@Photoshop Tricks!

All six trigonometric functions appear as distinct line-segment lengths on a single unit circle.

Sine and cosine are the same wave seen from a different perspective.

This is why circles, right triangles, sine, cosine, π and even waves are all related.

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