unit circle chart

  Trigonometric Functions and the Unit Circle We have already defined the trigonometric functions in terms of right triangles. In this section, we will redefine them in terms of the unit circle. Recall that a unit circle is a circle centered at the origin with radius 1. The angle [latex]t[/latex] (in radians ) forms an arc of length [latex]s[/latex]. The  x-  and  y- axes divide the coordinate plane (and the unit circle, since it is centered at the origin) into four quarters called quadrants. We label these quadrants to mimic the direction a positive angle would sweep. The four quadrants are labeled I, II, III, and IV. For any angle [latex]t[/latex], we can label the intersection of its side and the unit circle by its coordinates, [latex](x, y)[/latex]. The coordinates [latex]x[/latex] and [latex]y[/latex] will be the outputs of the trigonometric functions [latex]f(t) = \cos t[/latex] and [latex]f(t) = \sin t[/latex], respectively. This means: UNIT CIRCLE CHART [late...