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Rectangular to Polar Calculator
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The distance from x-axis and the y-axis located in the rectangular coordinate system can be represented as (x, y) coordinates. The x-coordinate and y-coordinate are the rectangular coordinate system.
The polar coordinate system is two dimensional which can be related and converted only to the other two dimensional coordinate systems alone. The coordinates used for the location of a point in the two dimensional rectangular coordinate system is (x, y). For the polar coordinate system it is (r, $\theta$).
Rectangular to Polar Calculator is used to convert Rectangular coordinates into polar coordinates.
 

Step by Step Calculation

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Step 1 :  

Observe the given rectangular coordinates(x, y).



Step 2 :  

To convert rectangular coordinates into polar coordinates use the condition:


r = $\sqrt{x^{2} + y^{2}}$


$\theta$ = $tan^{-1}(\frac{y}{x})$



Example Problems

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  1. Convert the rectangular coordinates (4, 3) in to it's polar coordinates?


    Step 1 :  

    Given rectangular coordinates = (4, 3) = (x, y)



    Step 2 :  

    Polar coordinates (r , $\theta$)


    r = $\sqrt{x^{2} + y^{2}}$ = $\sqrt{4^{2} + 3^{2}}$ = $\sqrt{16 + 9}$ = $\sqrt{25}$ = 5


    $\theta$ = $tan^{-1}(\frac{y}{x})$ = $tan^{-1}(\frac{3}{4})$ = 36.870 degrees



    Answer  :  

    (r, $\theta$) = (5, 36.870)



  2. Convert the rectangular coordinates (5, 4) in to it's polar coordinates?


    Step 1 :  

    Given rectangular coordinates = (5, 4) = (x, y)



    Step 2 :  

    Polar coordinates (r , $\theta$)


    r = $\sqrt{x^{2} + y^{2}}$ = $\sqrt{5^{2} + 4^{2}}$ = $\sqrt{25 + 16}$ = $\sqrt{41}$ = 6.40312424


    $\theta$ = $tan^{-1}(\frac{4}{5})$ = $tan^{-1}(\frac{4}{5})$ = 36.66 degrees



    Answer  :  

    (r, $\theta$) = (6.40312424, 36.66)



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