Is a sinusoid a function whose values repeat based on position of a point that moves around a circle

  yes

Step-by-step explanation:

One way to describe a sine function is that it is the y-coordinate of a point on the unit circle that is θ radians counterclockwise from the x-axis:

  y = sin(θ)

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Another way to describe the sine function is that it is the solution to the differential equation for undamped "simple harmonic motion."

  y'' + y = 0; y'(0) = 1, y(0) = 0

  y = sin(x)