# 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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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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Q5:

Convert the rectangular equation to the polar form.

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Q6:

Convert the polar equation to the rectangular 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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Q10:

Consider the rectangular equation .

Convert the given equation to the polar form.

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Which of the following is the sketch of the equation?

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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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