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Time is point rotation in a circle There are 2 other circles and 2 other point rotations around those circles that are all mutually perpendicular to each other, therefore separate dimensions. Since the circumference of the unit circle happens to be $ (2\pi)$, and since (in analytical geometry or trigonometry) this translates to $ (360^\circ)$, students new to. By unit circle, i mean a certain conceptual framework for many important trig facts and properties, not a big circle drawn on a sheet of paper that has angles labeled with. Maybe a quite easy question Why is $s^1$ the unit circle and $s^2$ is the unit sphere Also why is $s^1\\times s^1$ a torus It does not seem that they have anything. You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do i. 2 i just recently did a project on the unit circle and the three main trig functions (sine, cosine, tangent) for my geometry class, and in it i was asked to provide an explanation. We have been taught $\cos (0) = 1$ and $\sin (90) = 1$ But, how do i visualize these angles on the unit circle? I have found a interesting website in google It represents tangent function of a particular angle as the length of a tangent from a point that is subtending the angle.i thought it. Show that unit circle is not homeomorphic to the real line ask question asked 7 years, 3 months ago modified 5 years, 11 months ago If you're working with linear system, eigenvalues on unit circle still make system lyapunov stable, but system is no longer asymptotically lyapunov stable Loosely speaking, in linear case.