Special Trig Values: Multiples of π/6

To find the values of trig functions for multiples of $\frac{\pi}{6}$, we use right triangle trigonometry. Since $\frac{\pi}{6}=30^{\circ}$, it makes us think of a 30-60-90 triangle.

As you might recall, angle B is 30 degrees, angle A is 60 degrees, side AC has length 1, side AC has length $\frac{1}{2}$, and side BC has length $\frac{\sqrt3}{2}$. So, by our trig definitions (sine=opposite/hypotenuse, and cosine=adjacent/hypotenuse), we have that $\sin30^{\circ}=\cos60^{\circ}=\frac12$, and $\sin60^{\circ}=\cos30^{\circ}=\frac{\sqrt3}{2}$. Then we can easily find the other multiples of $\frac{\pi}{6}$ by using the unit circle.