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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**Q2: **

Convert into cartesian form.

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**Q3: **

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

First, use the fact that to eliminate .

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Now, use the fact that to eliminate .

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Finally, make the subject.

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**Q4: **

Convert the equation into polar form.

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