Meaning of negative angle

Question

If I consider $\alpha=-\frac{\pi}{3}$ this is exactly equal to $2\pi-\frac{\pi}{3}$? So the consider blu angle is equal to consider the red one?

Answer 1

• If we are talking about your special question:

When considering angles on the circle, you should see them modulo $2\pi$. Let $\alpha = -\frac{\pi}{3} $ and $\beta = 2\pi - \frac{\pi}{3}$. Since $\alpha \equiv \beta \pmod {2\pi}$ they will coincide on the circle.

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• If we are talking about the meaning of the negative angle in general:

These all are just an agreement of mathematicians (plus everyone else working in related fields).

For convenience, we say "rotate $-30^\circ$" instead of saying "rotate $30^\circ$ clockwise" or "rotate $300^\circ$"

So, whenever you see a negative angle, you should think of its direction.