Precalculus : Convert Polar Equations To Rectangular Form

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Convert Polar Equations To Rectangular Form

Convert from polar form to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by multiplying both sides by .

Keep in mind that 

Remember that 

So then,

Now, complete the square.

Example Question #2 : Convert Polar Equations To Rectangular Form

Convert the polar equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by multiplying both sides by .

Remember that 

Keep in mind that 

So then,

Now, complete the square.

This is a graph of a circle with a radius of  and a center at 

Example Question #3 : Convert Polar Equations To Rectangular Form

Convert the polar equation into rectangular form:

Possible Answers:

Correct answer:

Explanation:

Remember that 

So then  becomes

Now, multiply both sides by  to get rid of the fraction.

Since  the rectangular form of this equation is

Example Question #631 : Pre Calculus

Convert the polar equation into rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by using the double angle formula for .

Substitute that into the equation gives the following:

Because we need  and  to get  and  respectively, multiply both sides by .

Now, recall that .

Example Question #2 : Convert Polar Equations To Rectangular Form

Convert the polar equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by taking the tangent.

Recall that 

Example Question #633 : Pre Calculus

Convert the polar equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by taking the tangent.

Recall that 

Example Question #634 : Pre Calculus

Convert the polar equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Recall that 

Substituting this into the given equation gives

Multiply both sides by  to get rid of the fraction.

Recall that  and that 

Example Question #635 : Pre Calculus

Convert the polar equation into rectangular form:

Possible Answers:

Correct answer:

Explanation:

Recall that  and 

Multiply both sides by 

Recall that  and 

 

Example Question #3 : Convert Polar Equations To Rectangular Form

Convert the polar equation into rectangular form:

Possible Answers:

Correct answer:

Explanation:

Recall that 

Plugging this into the equation gives us

Multiply both sides by  to get rid of the fraction.

Recall that 

So then the rectangular form of the equation is 

Example Question #4 : Convert Polar Equations To Rectangular Form

Convert the polar equation into rectangular form.

Possible Answers:

Correct answer:

Explanation:

Recall that 

Multiply both sides by  to get rid of the fraction.

Recall that .

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