# Calculus 2 : Polar

## Example Questions

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### Example Question #1 : Polar

Rewrite the polar equation

in rectangular form.

Explanation:

or

### Example Question #1 : Polar Form

Rewrite in polar form:

Explanation:

### Example Question #2 : Polar

Rewrite the polar equation

in rectangular form.

Explanation:

### Example Question #1 : Polar

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

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

.

Explanation:

The point will have rectangular coordinates .

### Example Question #1 : Polar Form

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

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.

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.

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:

### Example Question #4 : Polar Form

What is the following coordinate in polar form?

Provide the angle in degrees.

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.

.

### Example Question #5 : Polar Form

What is the equation  in polar form?