# Why is cos -pi/6 the same as cos pi/6?

May 15, 2015

The cosine function is even, which means that $\cos \left(- x\right) = \cos \left(x\right)$.

In opposition, the sine function is odd, which means that $\sin \left(- x\right) = - \sin \left(x\right)$.

You can observe that on the trigonometric circle :

(source : http://en.wikipedia.org/wiki/Unit_circle)

You see that when you have an angle of $\frac{\pi}{6}$ or of $- \frac{\pi}{6} = \frac{11 \pi}{6}$, the abscissa (the $x$ position on the graph) $=$ the cosine value $= \frac{\sqrt{3}}{2}$ in both cases.

In opposition, the ordinate (the $y$ position on the graph)$=$ the sine value $= \frac{1}{2}$ with an angle of $\frac{\pi}{6}$ and $= - \frac{1}{2}$ with an angle of $- \frac{\pi}{6}$.