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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
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
Möbius transformation mapping - Mathematics Stack Exchange 7 For your first example, because the boundary of the upper half-plane is a "circle" (in the Riemann sphere sense (sorry, Riemann sphere, not Bloch sphere)), and the boundary of the unit disk is a circle (plainly, but also in the Riemann sphere sense), we try to map the boundary of the one to the boundary of the other
Show that unit circle is compact? - Mathematics Stack Exchange 22 Quick question Say we are given the unit circle $\ { (x,y)\in \mathbb {R}^2: x^2+y^2=1 \}$ Is this set compact? How can I prove that this is closed? Bounded? Do I have to take the complement of the set, showing that that set is open (and so unit circle is closed)? Any other trick?
How do you parameterize a circle? - Mathematics Stack Exchange Your parametrization is correct Once you have a parameterization of the unit circle, it's pretty easy to parameterize any circle (or ellipse for that matter): What's a circle of radius $4$? Well, it's four times bigger than a circle of radius $1$!
Why do we use the unit circle to solve for sin and cos I know that in a unit circle where the radius is always one, sin is equal to y and cos is equal to x But why do we use these values even when the radius or the hypothenuse of the triangle isn't equal to one
How do I get the slope on a circle? - Mathematics Stack Exchange The prior answers have all used calculus I'm going to post an answer using only trig The following diagram from Wikipedia's Trig Page is helpful However, that diagram also has a fault--the picture is very cluttered :) Thus, I've redrawn it for you, labeling the components important for this problem: Note that $\csc\theta$ returns the distance from the origin to the y-intercept of the