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Parametrizing a circle in a counterclockwise direction Whether or not the parametrization traces a circle in clockwise direction or anti-clockwise direction depents on the convention of handed-ness you are using for your Cartesian coordinate system
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
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 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
trigonometry - How to read negative radians in the interval . . . For the last, it sounds like you are talking about special angles that are shown on the unit circle $\frac {3\pi}2$ is straight down, along $-y$ Why would $-\frac {5\pi}3$ be next? It depends on what angles you think are special
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