The Amazing Unit Circle
Supplementary Angle Identities |

Two angles are |

To put the angle supplementary to θ in standard position, start by reflecting the angle θ in the y-axis. The angle BOQ is θ, so the angle AOQ measures π - θ = 180° - θ. Thus Q has coordinates (cos(π-θ),sin(π-θ)) = (cos(180°-θ),sin(180°-θ)). When a point (a,b) is reflected in the y-axis, it moves to 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 supplementary angle identities hold for all angles θ. Restore initial diagram |

The Amazing Unit Circle |
Trigonometry Facts |
Home Page |
Privacy Policy |