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Vectors notations.

  • Thread starter Llama77
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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,
 

Answers and Replies

cristo
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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.
 
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I know that already, but why do we need to use a arctan instead of just the standard tan.
 
cristo
Staff Emeritus
Science Advisor
8,056
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I know that already, but why do we need to use a arctan instead of just the standard tan.
arctan is the inverse operator of tan, otherwise written as tan-1. So, given the equation tanθ=ay/ax, taking the inverse tangent of each side, we obtain arctan(tanθ)=arctan(ay/ax) => θ= arctan(ay/ax).
 

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