What associated arcs are

Associated arcs are “relatives” of an angle $\alpha$ obtained by elementary symmetries on the unit circle. 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 ($0\le\alpha\le\pi/2$), where the special values are used.

The four main types of associated arcs correspond to as many symmetries: opposite angles (symmetry about the $x$-axis), supplementary ones (about the $y$-axis), those differing by $\pi$ (about the origin) and complementary ones (about the bisector $y=x$).

Links

Topics: Trigonometry
Concepts: Associated arcs · Unit circle