The Amazing Unit Circle
Opposite Angle Identities |

By |

The angle opposite θ has measure θ + π = θ + 180°. Thus Q has coordinates The point on the opposite side of the unit circle from (a,b) is the point (-a,-b). So Q also has coordinates (-cos(θ),-sin(θ)). Therefore:
or
These are the Although the diagram shows the angle θ in the first quadrant, the same conclusion can be reached when θ lies in any quadrant, and so the opposite angle identities hold for all angles θ. Restore initial diagram |

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