# Worksheet: Conversion between Rectangular and Polar Equations

In this worksheet, we will practice converting equations from polar to rectangular form and vice versa.

**Q1: **

Consider the polar equation . Complete the following steps to help you find the Cartesian form of the equation by writing an equivalent equation each time.

Multiply both sides of the equation through by .

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Use the fact that to simplify the expression.

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Given that and , we can use the Pythagorean theorem to show that . Use this to eliminate the in the previous expression.

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**Q4: **

Convert the equation into polar form.

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**Q7: **

Convert the rectangular equation to the polar form.

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**Q8: **

Convert the polar equation to the rectangular form.

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**Q9: **

Convert the polar equation to the rectangular form.

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**Q11: **

Convert into Cartesian form.

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**Q12: **

Convert into Cartesian form.

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**Q13: **

Convert into polar form.

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**Q14: **

Convert into polar form.

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**Q15: **

Convert into Cartesian form.

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