If it is in rectangular form, your goal is to only have rs and θs. If your equation is in polar form, your goal is to convert it in such a way that you are only left with xs and ys. If it contains xs and ys, it is in rectangular form. If it contains rs and θs, it is in polar form. Similarly, converting an equation from polar to rectangular form and vice versa can help you express a curve more simply.įollow these five steps to convert equations between the polar and rectangular systems: Step 1: Identify the form of your equationĪ quick glance at your equation should tell you what form it is in. So, although polar coordinates seem to complicate things when you are first introduced to them, learning to use them can simplify math for you quite a bit! If we were to express it in rectangular coordinates, the calculation would require a few extra steps. If we wanted to move the dot to the 30° line, while maintaining our distance of 5 units from the origin (the blue dot), we could simply express it as (5,30°) or (5,𝝅/6) in polar coordinates.
Where would you put the point (3,4)? If you would put it by the red dot, you’re correct.īy now, you know that the red dot can also be represented as (5,0.92) in polar coordinates. Ignore the circles on the plot for a second and picture the rectangular system you’re familiar with. Polar coordinates exist to make it easier to communicate where a point is located. Why do Polar Coordinates and Equations exist? Today, I’ll discuss a foolproof method - Cambridge Coaching’s Five Step Process for converting polar to Cartesian equations. In fact, you’ve been learning them for years you have just been using them differently.
And I have good news! You already have all the tools you need to learn to express equations in polar form. Remember the first time you saw an equation and were introduced to these strange x and y variables? It may seem like second nature now, but you were learning about a whole new way to communicate about points and curves. If polar equations have you second-guessing your future as a nuclear physicist, fret not! Almost every pre-calculus student I have tutored has struggled here, and it isn’t surprising at all.
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