How to best explain sine and cosine on the unit circle
Jun 4, 2025 · 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 …
calculus - Trigonometric functions and the unit circle
Aug 27, 2022 · 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 …
Tips for understanding the unit circle - Mathematics Stack Exchange
Nov 21, 2012 · 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 …
How does $e^{i x}$ produce rotation around the imaginary unit …
The only thing that is changed is x x, now if we assign coordinates to real (cos x (cos x) as x x -coordinate and complex value (sin x) (sin x) as y y -coordinate (or imaginary axis), then this is …
general topology - Why do we denote $S^1$ for the the unit …
Maybe a quite easy question. Why is S1 S 1 the unit circle and S2 S 2 is the unit sphere? Also why is S1 ×S1 S 1 × S 1 a torus? It does not seem that they have anything in common, do they?
Show that unit circle is not homeomorphic to the real line
May 12, 2018 · Show that unit circle is not homeomorphic to the real line Ask Question Asked 7 years, 8 months ago Modified 6 years, 4 months ago
Can we characterize the Möbius transformations that maps the …
Oct 8, 2012 · The function f f maps unit circle to unit circle and a a to 0 0. Every Möbius transformation that preserves the unit disk must be of the above form. The second statement …
On Cotangents, Tangents, Secants, And Cosecants On Unit Circles.
Jun 25, 2018 · Above is a diagram of a unit circle. While I understand why the cosine and sine are in the positions they are in the unit circle, I am struggling to understand why the cotangent, …
Understanding the Unit Circle - Mathematics Stack Exchange
See the StackExchange thread Tips for understanding the unit circle, and note the distinction I make in my answer between what students often see as the unit circle and what teachers see …
How does e, or the exponential function, relate to rotation?
First, assume the Unit Circle Parameter is Time in Seconds. The essential idea is that in order for a Radius of Length 1 to move 1 Arc Length in 1 Second it is required to have a Velocity of 1, …