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Polar to Rectangular Conversions

Convert from polar to cartesian coordinates

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Practice Polar to Rectangular Conversions
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Polar Graph Conversions

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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 =_________________

r^2 =_________________                tan\theta =_________________


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

  1. (3, \frac{\pi}{3})
  2. (2, \frac{3\pi}{2})
  3. (5, \frac{\pi}{4})

Write each polar equation in rectangular form:

  1. r=4\cos \theta
  2. r=10\sin \theta
  3. r=5\csc \theta


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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 \pi radians must be added to the value of \theta 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 where0\leq \theta \leq 2\pi .

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 = r \cos \theta and y = r \sin \theta.

  1. 2x-y=6
  2. 3x+4y=2
  3. (x+2)^2+y^2=4
  4. (x+5)^2+(y-1)^2=26
  5. x^2+(y-6)^2=36
  6. x^2+(y+2)^2=4
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