Question

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

Answer 1

The cosine function is even, which means that `cos(-x) = cos(x)`.

In opposition, the sine function is odd, which means that `sin(-x) = -sin(x)`.

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 `pi/6` or of `-pi/6 = (11pi)/6`, the abscissa (the `x` position on the graph) `=` the cosine value `= sqrt3/2` in both cases.

In opposition, the ordinate (the `y` position on the graph)`=` the sine value `=1/2` with an angle of `pi/6` and `=-1/2` with an angle of `-pi/6`.