Calculus 2 : Polar

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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Example Question #1 : Polar

Rewrite the polar equation 

in rectangular form.

Possible Answers:

Correct answer:

Explanation:

or 

Example Question #1 : Polar

Rewrite in polar form:

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Polar

Rewrite the polar equation 

in rectangular form.

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Polar

Give the polar form of the equation of the line with intercepts .

Possible Answers:

Correct answer:

Explanation:

This line has slope  and -intercept , so its Cartesian equation is .

By substituting, we can rewrite this:

Example Question #1 : Polar

Give the rectangular coordinates of the point with polar coordinates 

.

Possible Answers:

Correct answer:

Explanation:

The point will have rectangular coordinates .

Example Question #1 : Polar

What would be the equation of the parabola  in polar form?

Possible Answers:

Correct answer:

Explanation:

We know  and .

Subbing that in to the equation  will give us .

Multiplying both sides by  gives us 

.

Example Question #2 : Polar Form

A point in polar form is given as .

Find its corresponding  coordinate.

Possible Answers:

Correct answer:

Explanation:

To go from polar form to cartesion coordinates, use the following two relations.

In this case, our  is  and our  is .

Plugging those into our relations we get 

which gives us our  coordinate.

Example Question #3 : Polar Form

What is the magnitude and angle (in radians) of the following cartesian coordinate?

Give the answer in the format below.

Possible Answers:

Correct answer:

Explanation:

Although not explicitly stated, the problem is asking for the polar coordinates of the point . To calculate the magnitude, , calculate the following:

To calculate , do the following:

 in radians. (The problem asks for radians)

 

Example Question #2 : Polar Form

What is the following coordinate in polar form?

Provide the angle in degrees.

Possible Answers:

Correct answer:

Explanation:

To calculate the polar coordinate, use

However, keep track of the angle here. 68 degree is the mathematical equivalent of the expression, but we know the point (-2,-5) is in the 3rd quadrant, so we have to add 180 to it to get 248.

Some calculators might already have provided you with the correct answer.

.

Example Question #3 : Polar Form

What is the equation  in polar form?

Possible Answers:

Correct answer:

Explanation:

We can convert from rectangular form to polar form by using the following identities:  and . Given , then .

. Dividing both sides by ,

 

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