gentlemenMGOUFFE: some corresponding points can be the the positive ray of the number line making a single rotation about the circle.
l337hitchhiker: who is this
gentlemenMGOUFFE: each point on the circle determines the terminal ray of a central angle of a circle. the radian measure of an angle in standard position is equal to the coordinate of the corresponding point on the number line.
gentlemenMGOUFFE: for example, a point whose coordinate is 2 on a number line corresponds to a point on the unit circle that determines an angle whose radian measure is 2.
l337hitchhiker: who the hell is this
gentlemenMGOUFFE: similarly, a point whose coordinate is pi/2 (approx. 1.5708) on the number line corresponds to a point on the unit circle that determines an angle whose radian measure is pi/2, that is, a right angle
l337hitchhiker: so whats the point\
gentlemenMGOUFFE: we can continue to wrap the positive ray of the number line about the circle in a counterclockwise direction.
gentlemenMGOUFFE: in the same way, we can wrap the negative ray of the number line about the circle in a clockwise direction.
gentlemenMGOUFFE: and under this wrapping function, every point on the real-number line corresponds to one, and ONLY ONE point on that circle.
gentlemenMGOUFFE: do you understand?
l337hitchhiker: to an extant enough to know part of it
l337hitchhiker: but who hte hell are you
gentlemenMGOUFFE: very good... moving on...
gentlemenMGOUFFE: there is, however, an infinite number of points on the real-number linethat correspond to the same point on the unit circle.
gentlemenMGOUFFE: would you like an example?
gentlemenMGOUFFE: the points that represent the real numbers 0, 2pi, -2pi, 4pi, -4pi, 6pi, -6pi, and so on, all correspond to point (1, 0) on the circle, that is, the point thst determines a central angle of 0 radian.
gentlemenMGOUFFE: this set of real numbers is indicated by the expression 2piK, where K represents any integer.
gentlemenMGOUFFE: is it all sinking in? because it's going to get a bit harder now.
l337hitchhiker: one more time old man npc
gentlemenMGOUFFE: tough luck... anyway, as i was saying...
gentlemenMGOUFFE: in the same way, the set of points whose real numbers are of the form 2+2piK for all integral values of k corresponds to a point on the unit circle that determines a central angle of 2 radians.
gentlemenMGOUFFE: we will use this correspondence between points on the real-number line and the radian measures of angles of a unit circle to graph trigonometric functions.
gentlemenMGOUFFE: and that concludes our lesson.
gentlemenMGOUFFE: dont forget to study, fishlips
l337hitchhiker: ok so who is this
gentlemenMGOUFFE: professor m. gouffe