The Amazing Unit Circle
Definitions of Sine and Cosine |

The trigonometric functions sine and cosine are defined in terms of the coordinates of points lying on the unit circle x Start by constructing the ray from the origin at angle θ (measured counter-clockwise from the positive x-axis). This ray meets the unit circle at a point P = (x,y). |

Cosine of the angle θ is cos(θ) = x.
Sine of the angle θ is sin(θ) = y. As θ changes so does the position of the point P and thus the values of cos(θ) = x and sin(θ) = y also change. In this way the Right away the unit circle gives us properties of the cosine and sine functions. Since the point P lies on the unit circle, both the cosine and sine functions have cos(0) = cos(0°) = 1 and sin(0) = sin(0°) = 0 cos(π/2) = cos(90°) = 0 and sin(π/2) = sin(90°) = 1 cos(π) = cos(180°) = -1 and sin(π) = sin(180°) = 0 cos(3π/2) = cos(270°) = 0 and sin(3π/2) = sin(270°) = -1 By using the geometric properties of the unit circle definition we can easily discover many other properties of the trigonometic functions. We look at many of these properties in the other parts of this unit circle activity. |

The Amazing Unit Circle |
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