Sinusoidal and Circular Motion

Consider a vector of length one (1), rotating at a steady speed in a plane, the vector tracing a circle with a radius equal to its length.

Figure 7: A vector rotating along the unit circle.
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Each time the vector completes one rotation of the circle, it has completed a cycle of $2\pi$ .
The rate at which the vector completes one cycle is given by its frequency.
The length of the vector is given by its amplitude (which for simplicity, in this case, is one (1)).

**Figure 7:** A vector rotating along the unit circle.
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``Music 270a: Sinusoids'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).