Question:
The angle between two vectors $\vec{P}$ and $\vec{Q}$ is $\alpha$. If $\tan\alpha=-\sqrt{3}$, determine $\alpha$.
My attempt:
$$\tan\alpha=-\sqrt{3}$$
$$\alpha=\tan^{-1}(-\sqrt{3})$$
$$\alpha=-60^{\circ}$$
My book's attempt:
$$\tan\alpha=-\sqrt{3}$$
$$\tan\alpha=-\tan(60^{\circ})$$
$$\tan\alpha=\tan(180^{\circ}-60^{\circ})$$
$$\tan\alpha=\tan(120^{\circ})$$
$$\alpha=120^{\circ}$$
Addendum:
Interestingly enough, $-60^{\circ}$ and $120^{\circ}$ are describing two different cases. If the answers were $120^{\circ}$ and $-240^{\circ}$, I would've had no problem as they are both describing the same case, unlike here. Here, $-60^{\circ}$ and $120^{\circ}$ are describing two different things and they both can't be correct.
My question:
Whose answer is correct, mine or my book's? I know that there's a rule stating that the angle between two vectors can' be greater than $180^{\circ}$. Is there another rule that states that the angle between two vectors can't be less than $0^{\circ}$?
