Read about them before asking us.

Differences

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In therectangular coordinatesystem, the one you love and use all the time a point is determined by its vertical distance and horizontal distance. So means 1 unit to the left and 2 up.

In thepolar coordinatesystem, which because more popular in Calculus, a point is determined by itsangleit makes with the x-axis (the counterclockwise angle, like in trigonometry) and its length (basically its radius). For example, means a point which makes and angle of and whose lengh is one. Can you find an equivalent in rectangular coordinates? Yes. It is . What about a little bit more though suggests that is that point. That is the idea of this coordinate system.

Now we cannotconversion formulato convert from one coordinate system to another.

The rules are as follows,

See if you can show why these formulas are right.

Some graphs look simpler in polar coordinates and some look simpler in rectangular coordinates.

First what does it means "a graph in polar coordinates"? It means the same thing as in rectangular. Just pick several 's and find their cooresponding 's and connect the dots.

For example, is a circle in rectangular coordinates. But using the conversion formula we get, thus, . So the graph in polar form is a circle, look how much easier it looks!

Now let us show when polar form is worse. For example, is a basic simple honest horizontal line. But if we use the conversion formulas we get thus . Look how it overcomplicates it.