Negative Angles

A negative angle turns clockwise. The point at -30° is the point at 30° reflected in the x-axis: the same distance across, the same distance down as the other is up.

Reflecting in the x-axis keeps x and flips the sign of y.

So $\cos\left(-30^{\circ}\right) = \frac{\sqrt{3}}{2}$, the same as cos 30°, while $\sin\left(-30^{\circ}\right) = \frac{-1}{2}$, the opposite of sin 30°. The reflection works for every angle, which gives three identities (the last wherever tan x is defined):

$$\cos\left(-x\right) = \cos\left(x\right)$$

$$\sin\left(-x\right) = -\sin\left(x\right)$$

$$\tan\left(-x\right) = -\tan\left(x\right)$$

A function that ignores the sign of its angle, like cosine, is called even; one that passes the sign through, like sine and tangent, is odd.