I'm writing a PHP algorithm to calculate the sum of two 2D vectors with the same origin, given their intensity and their angle with a given axis. How to calculate the properties of the sum vector? I have some ideas about the intensity (Pythagorean theorem and Carthesian components), but I don't have a clue of how to calculate the angle.
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If your resultant vector is $c$ and $\hat c = c/|c|$, then $\hat c \cdot \hat x = \cos \theta$ and $\hat c \cdot \hat y = \sin \theta$, where $\hat x, \hat y$ are the unit vectors in the x- and y-directions and $\theta$ is the angle $c$ makes with respect to the x-axis.