Associated arcs

Associated arcs are “relatives” of an angle $\alpha$ obtained by elementary symmetries on the unit circle: opposite angles, supplementary ones, those differing by $\pi$, complementary ones. Knowing how $\sin,\cos,\tan$ behave under these symmetries lets us reduce the computation of any angle to the case of an angle in the first quadrant.

• What associated arcs are
• Opposite arcs
• Supplementary arcs
• Arcs differing by pi
• Complementary arcs
• How to reduce an angle to the first quadrant
• Reading the solutions off the graph