RJM's Demo of 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).
The peak amplitude of the sinusoid equals the radius of the circle. How many times it repeats per second is its frequency.
One revolution is 2π radians - which is why engineers often use angular frequency ω = frequency * 2 π.
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, by adjusting the sliders.
When you stop moving a slider, the sinusoid is drawn slowly both as a plot versus time, and moving round the circle.
© Dr Richard Mitchell, Jul 2014 Cybernetics at Systems Engineering Email Comments