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This visual shows how sine of θ varies on the unit circle.

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Massimo

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94,479 views • 8 months ago •via X (Twitter)

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Euler's formula states that e^(iθ) = cos θ + i sin θ. As the angle θ increases, e^(iθ) traces the unit circle in the complex plane. Plotted against θ, that rotation becomes a helix. The real part of the helix projects as the cosine wave Re(z) = cos θ. The imaginary part projects as the sine wave Im(z) = sin θ.
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Euler's formula states that e^(iθ) = cos θ + i sin θ. As the angle θ increases, e^(iθ) traces the unit circle in the complex plane. Plotted against θ, that rotation becomes a helix. The real part of the helix projects as the cosine wave Re(z) = cos θ. The imaginary part projects as the sine wave Im(z) = sin θ.

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