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So... in school we are seeing first grade equations and the polar coordinate system. We were watching how to transport one from another... and I wondered how equations looked like in the polar coordinate system. We have already seen how they look like or to interpret some of its behavior in the Cartesian Plane, but not in the polar. So my question is, how do equations look like in the polar system and how can we interpret them?

(I barely know about Calculus, which makes me feel like a moron. I am mostly self-taught but it's very hard for me so please, if you use Calculus to explain the idea be as clear as possible, I know it's a lot to ask but I have this idea and I am not really sure how to proceed)

Best regards! Have a nice day!

Note by Karen Sarai Morales Montiel
2 weeks, 6 days ago

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A polar form of an equation is basically, another way to view a system of equations (a graph in the coordinate plane). Instead of viewing the graph of the equation on a sheet of paper and analysing it along the horizontal and vertical dimensions (length), we consider ourselves to be a point object located at the origin of the coordinate system and looking at the graph of the equation that will be in our plane. So, in this case, the only possible way of differentiating between two different points its the points, distance from us (origin) and the direction of that point. The direction of the point is indicated by the angle the point makes with the x-axis. So, no two distinct points can have the same set of parameters (distance and direction).

As, an example, consider the equation $$x^2 + y^2 = 1$$. Here is how the graph is plotted:-

So, here for a particular point A, the distance parameter is the distance from the origin i.e $$AB$$ which happens to be $$1$$ here, and the direction is the angle $$\angle BAC$$ which here is $$45°$$.

- 2 weeks, 2 days ago

Thank you!...Although I don't see the graph...

- 2 weeks, 2 days ago

Refresh your page, there is one in my comment.

- 2 weeks, 2 days ago

Thanks!

- 2 weeks, 1 day ago