How to convert polar equations into rectangular equations
Formulas for converting polar equations into rectangular equations
To convert polar equations to rectangular equations, we’ll use the following conversion formulas.
???x=r\cos{\theta}???
???y=r\sin{\theta}???
???r^2=x^2+y^2???
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Converting equations in polar coordinates into an equation in rectangular coordinates
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Let’s do one more example where we convert a polar equation into a rectangular equation
Example
Convert the polar equation to a rectangular equation.
???r=3\cos{\theta}???
Modify the conversion formula ???x=r\cos{\theta}???.
???x=r\cos{\theta}???
???\cos{\theta}=\frac{x}{r}???
Once we’ve eliminated all r and theta variables, and replaced them with x and y variables, we’re done with the conversion.
Plug this into the given polar equation.
???r=3\left(\frac{x}{r}\right)???
???r^2=3x???
Use ???r^2=x^2+y^2???.
???x^2+y^2=3x???
???x^2-3x+y^2=0???
Once we’ve eliminated all ???r??? and ???\theta??? variables, and replaced them with ???x??? and ???y??? variables, we’re done with the conversion.
