# Vectors notations.

So I am in a Calculus based Physics course and had some questions about converting to and from the component notation and the magnitude-angle notation.

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,

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cristo
Staff Emeritus
A vector can be written in component form as a=(ax,ay). The components of a vector can be found by constructing a right angled triangle and using trigonometry. As an example, consider the vector a at an angle θ from the horizontal. Now consider drawing a line from the end of the vector, down to the x axis. We now have a triangle involving the magnitude of a as the hypotenuse, and ax and ay, the magnitude of the components.

Using trigonometry on the triangle we can obtain ax=acosθ (where a is the magnitude of a) and tanθ=ay/ax.

I know that already, but why do we need to use a arctan instead of just the standard tan.

cristo
Staff Emeritus