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# Rectangular to Polar Conversions

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Practice Rectangular to Polar Conversions
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Polar Graph Conversions

### Vocabulary

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:

$x =$ _________________                $y =$_________________

$r^2 =$_________________                $tan\theta =$_________________

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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.

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Write the following points, given in rectangular form, in polar form using radians where$0\leq \theta \leq 2\pi$ .

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. $x^2+(y+2)^2=4$