Averaging Coordinates

Question

If I have:

Mag and Pha Values in a circle of

M-P (.049, 164) (.0139, 167) (.041, 355)

I am treating M as a Radial Point (Distance From The Center) and P as the Angle How do I average these 3 for the average coordinate.

Answer 1

I'd convert the points to Cartesian coordinates through $x=r\cos\theta$ and $y=r\sin\theta$ and average those by averaging the $x$ components and $y$ components separately. (It looks like you're using degrees for the angles; make sure you calculate $\sin$ and $\cos$ correctly!) Then I'd convert the averaged point back to polar coordinates by $r=\sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}(y/x)$ (taking into account the quadrant).