Precalculus : Polar Coordinates

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Convert Polar Coordinates To Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question, 

The rectangular coordinates are 

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

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 #1 : Polar Coordinates

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 #1 : Polar Coordinates

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 #1 : Polar Coordinates

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 : Polar Coordinates

Convert the polar equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by taking the tangent.

Recall that 

Example Question #1 : Polar Coordinates

Convert the polar equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

Start by taking the tangent.

Recall that 

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

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 #1601 : 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 #1 : Convert Polar Equations To Rectangular Form And Vice Versa

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 

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