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What are polar coordinates?

People doing mathematics at A-Level will be familiar with the concept of using x and y coordinates in the cartesian coordinate system. But introducing the idea of the polar coordinate system can be confusing to some.

In the polar coordinate system, instead of using a square grid to plot points on, you use a circular grid. The centre of the grid is known as the pole.

Also, instead of the two axes we are familiar with, there is just one in the polar system. This axis is known as the initial line, and bears similarity to the positive x-axis in the cartesian system.

Know that we have the polar grid explained, we need to know how to plot coordinates upon it.

A polar coordinate can be plotted by knowing its magnitude and angle. The magnitude of a polar point is its distance from the pole and is represented by the letter r​.

The angle of a polar point is the angle between the initial line and a figurative line joining the point to the pole, and is measured anticlockwise from the intial line, and is measured in radians. The angle is denoted by θ​​.

So in summary, polar coordinates use a circular grid and can be shown in the form (r, θ).

Alex W. A Level Maths tutor, GCSE Maths tutor, A Level Further Mathem...

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