- calculus - Trigonometric functions and the unit circle - Mathematics . . .
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 Calculus are taught about radians, which is a very confusing and ambiguous term
- Tips for understanding the unit circle - Mathematics Stack Exchange
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 degree measures 30, 45, 60, 90, 120, 150, etc (and or with the corresponding radian measures), along with the exact values for the sine and cosine of these angles
- general topology - Why do we denote $S^1$ for the the unit circle and . . .
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
- How does $e^ {i x}$ produce rotation around the imaginary unit circle?
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
- Can we characterize the Möbius transformations that maps the unit disk . . .
So the answer is that the Möbius transformations sending the unit circle to itself are precisely the Möbius transformations sending the unit disc to itself, and their multiplicative inverses
- trigonometry - In the unit circle, how are sine and cosine values . . .
I do understand that the unit circle has a radius of 1 and sides of triangles made within it must pertain to the pythagorean theorem (hence these values with radicals, for accuracy), but that is all I understand How would one know to put exactly $\frac {\sqrt 3} {2}$ for the sine of $\frac {\pi} {3}$ radians? This is unclear to me
- Show that unit circle is not homeomorphic to the real line
Show that unit circle is not homeomorphic to the real line Ask Question Asked 7 years, 6 months ago Modified 6 years, 2 months ago
- 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, Acceleration of 1, Jolt of 1, etc
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