ilovetoflyfpv:
So a pure sine wave is a graphed unit circle?
The answer to that is .... no.
However, if an object is moving around a circle repeatedly, then then a plot of the vertical distance (or even the horizontal distance) versus time will have a sine-wave pattern. Another way to convey that is ..... consider a circle. A plot of the y-axis value (of a point) versus the angle of that point will result in a sine wave pattern for the plot. So, it could be considered as a plot of a value versus angle in one case. Or, if we follow an object that travels around a circle, it could be considered as a plot of a value versus time.
For constant speed (constant angular velocity) motion around a circular path...... the angle and the time are related by this formula..... ANGLE (in radians) = w.t
'w' is 'omega'.... units of radians per second.
The above formula is under the assumption that the object's initial position on the circle (at time t = 0) is at zero degrees (or zero radians).
See this image obtained from the internet....
It means, you can model (mathematically) a sinewave by using some mathematical formulas that express the time-changing vertical (or even horizontal) distance as a function of time. The origins of such a model is circular motion. The cyclic nature of the circular movement links nicely with the cyclic nature of the sinewave. It does not necessarily mean that any real (measured) sinewave originates from circular motion. Sometimes....maybe - such as angular measurements for a motor shaft.... but not always.