# Cosine question. Scalar product.

1. Oct 12, 2014

### LagrangeEuler

1. The problem statement, all variables and given/known data
Find angle between vectors if
$$\cos\alpha=-\frac{\sqrt{3}}{2}$$

2. Relevant equations

3. The attempt at a solution
Because cosine is negative I think that $$\alpha=\frac{5\pi}{6}$$. But also it could be angle $$\alpha=\frac{7\pi}{6}$$. Right? When I search angle between vectors I do not need to write $$+2k\pi$$ where $$k$$ is integer. Right? Thanks for the answer.

2. Oct 12, 2014

### Staff: Mentor

I'd say you're right. The dot product of two unit vectors giving a negative cosine just means the angle between them is greater than 90 degrees and if you look at a diagram of the two possible angles you'll see they are symmetrical about a line thru one of the vectors.

3. Oct 12, 2014

### LagrangeEuler

Maybe only is important to look arccos as function? So answer is only $$\alpha=\frac{5\pi}{6}$$?
So if I look at calculator is $$\alpha=arccos(...)$$ is this $$\alpha$$ angle from $$[0,\pi]$$ or from $$[-\pi,\pi]$$.

Last edited: Oct 12, 2014
4. Oct 12, 2014

### Staff: Mentor

Looks fine to me. If you have two rays that emanate from the same point, two angles are determined- a smaller one and a larger one (I'm assuming here that the two rays don't point in exactly opposite directions). For problems asking about the angle between the two rays, they're usually interested in the smaller of the two angles.