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The first is if I am in the magnitude-angle notation, in a Cartesian cordiante system, will it always be ax=a cos(theta) to get the x component and ay=a sin(theta) to get the 7 component. I am asking because I am a little confused, lets day if the vector is ib the negative quadrant 4, do we sill do the same process.

Secondly when going from components to magnitude-angle notation, we use arctan(ay/ax) to get the angle theta. But what I don't get is why, the book just says tan(theta)=(ay/ax) and though I know enough since I have been told to use the arctan, I dont know why we use it or why the book doesn't say this,