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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
Show that unit circle is not homeomorphic to the real line is closed in R2 R 2 Set S1 S 1 is also bounded, since, for example, it is contained within the ball of radius 2 2 centered at 0 of R2 R 2 (in the standard topology of R2 R 2) Hence it is also compact However real line R1 R 1 is not because there is a cover of open intervals that does not have a finite subcover For example, intervals (n−1, n+1) , where n takes all integer values in Z Z, cover R R but there is no finite subcover Hence S1 S 1 can not be isomorphic to R1 R 1 How to show
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
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
How to find terminal point coordinates on a unit circle? Hey everyone I am working on a homework assignment which covers unit circles However I am really confused and having a lot of trouble locating terminal point coordinates Everything I have read on