”Determine

Points on the unit circle are given by the coordinates $(\cos(\theta), \sin(\theta))$, where $\theta$ ranges from

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$ to $2\pi$.

One pattern to observe is that for every angle $\theta$:

$ \cos(\theta + 2n\pi) = \cos(\theta) $

$ \sin(\theta + 2n\pi) = \sin(\theta) $

where $n$ is an integer. This periodicity shows that the points repeat every $2\pi$.

To understand the pattern, consider the coordinates $(cos( heta), sin( heta))$ for $ heta$ in $[0, 2pi]$.

We observe periodicity for $2pi$:

$ cos( heta + 2npi) = cos( heta) $

$ sin( heta + 2npi) = sin( heta) $

Points follow the coordinates $(cos( heta), sin( heta))$ with $ heta$ in $[0, 2pi]$:

$ cos( heta + 2npi) = cos( heta) $

$ sin( heta + 2npi) = sin( heta) $

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