Given the vector $\vec{A}=2 \vec{i} + 3\vec{j},$ the angle between $\vec{A}$ and $Y$ axis is?

Question

Would it be the inverse of $\tan 2/3$? I would be really grateful if someone could do the whole problem.

Thank you so much.

Answer 1

If you look at the triangle below the answer is a direct consequence of the definition of tangent, isn't it?:

Answer 2

The angle between $\;2\,\vec i+3\,\vec j\;$ and the positive direction of the $\;x$-axis is $\;\arctan\frac32\;$ (prinicpal value). Now you deduce what's the angle between the same vector and the positive direction of the $\;y$-axis.