- 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
- 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
- general topology - Why do we denote $S^1$ for the the unit circle and . . .
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?
- 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
- Notation of a Unit Circle: Does $S^1$ only mean a unit circle? Or does . . .
It so happens that the 1-dimensional sphere and the 1-dimensional torus are both the same object, namely a circle, and that the group of rotations of $\mathbb {R}^2$ can also be identified with a circle
- 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, 7 months ago Modified 6 years, 2 months ago
- Unit Circle - Overview - Numerade
In mathematics, the unit circle is a circle with a radius of one Frequently, especially in trigonometry and geometry, the unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system in the Euclidean plane The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere
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