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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
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
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
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
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 as the unit circle