The Circular Function Sin

Sin is a 'circular' function - as you rotate around a circle, radius r, the height of a point at angle φ is r*sin(φ).

Its peak amplitude equals the radius of the circle. How many times it repeats per second is its frequency, f.

One revolution is 2π radians - so engineers often use angular frequency ω = 2 π * f.

The sinusoid is plotted as a function of time : r sin(ω t + φ), and can also be represented as a line of length r at angle φ.

You can change the sinusoid's amplitude, the phase (which sets its initial value) and angular frequency, using the sliders. When you stop moving a slider, the sinusoid is drawn both as a plot versus time, and moving round the circle.

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