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Rectangular to Polar Conversions

Convert from cartesian to polar coordinates

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Practice Rectangular to Polar Conversions
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Polar Graph Conversions


Explain how to graph rectangular coordinates: _______________________________________________________________________

Explain how to graph  polar coordinates:


Polar to Rectangular Conversion

We can use trigonometry to convert from polar coordinates to rectangular coordinates.

Complete the coordinate conversion equations:

x= _________________                y=_________________

r2=_________________                tanθ=_________________


Given the following polar coordinates, find the corresponding rectangular coordinates of the points:

  1. (3,π3)
  2. (2,3π2)
  3. (5,π4)

Write each polar equation in rectangular form:

  1. r=4cosθ
  2. r=10sinθ
  3. r=5cscθ


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Rectangular to Polar Conversion

To convert from rectangular to polar coodinates, we use the Pythagorean Theorem and the Arctangent function.

Note: The Arctangent function only calculates angles in the first and fourth quadrants so π radians must be added to the value of θ for all points with rectangular coordinates in the second and third quadrants.


Write the following points, given in rectangular form, in polar form using radians where0θ2π .

Remember: There are many possible polar coordinates!

  1. (5,3)
  2. (-2,4)
  3. (-7,1)
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For each equation, convert the rectangular equation to polar form.

Hint: Use the equations x=rcosθ and y=rsinθ.

  1. 2xy=6
  2. 3x+4y=2
  3. (x+2)2+y2=4
  4. (x+5)2+(y1)2=26
  5. x2+(y6)2=36
  6. x2+(y+2)2=4
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