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Polar to Rectangular Calculator
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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, $\theta$).

Conversion from rectangular to polar coordinates:
The relations used for the conversion of the coordinates for the location of a point in the cartesian coordinate system to the polar coordinate system are,
r = $\sqrt{x^{2} + y^{2}}$
$\theta$ = $\tan^{-1}(\frac{y}{x})$

Conversion from polar to rectangular coordinates
:
The relations for converting the polar coordinates to the rectangular coordinates are,
x = r cos$\theta$
y = r sin$\theta$

Polar to Rectangular Calculator
is used to to convert polar coordinates into it's respective rectangular or cartesian coordinates.
 

Step by Step Calculation

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Step 1 :  

Observe the given polar coordinates.



Step 2 :  

To convert polar coordinates into rectangular coordinates use the condition:


x = r cos$\theta$


y = r sin$\theta$



Example Problems

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  1.  Convert the polar coordinates (7.5, 66) into it's respective rectangular coordinates?


    Step 1 :  

    Given polar coordinates (r, $\theta$) = (7.5, 66)



    Step 2 :  

    Rectangular coordinates (x, y)


    x = r cos$\theta$ = 7.5 cos 66 = 3.051


    y = r sin$\theta$ = 7.5 sin 66 = 6.852



    Answer  :  

    (x, y) = (3.051, 6.852)



  2.  Convert the polar coordinates (8.5, 45) into it's respective rectangular coordinates?


    Step 1 :  

    Given polar coordinates (r, $\theta$) = (8.5, 45)



    Step 2 :  

    Rectangular coordinates (x, y)


    x = r cos$\theta$ = 8.5 cos 45 = 6.010


    y = r sin$\theta$ = 8.5 sin 45 = 6.010



    Answer  :  

    (x, y) = (6.010, 6.010)



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