# AP Calculus BC : Functions, Graphs, and Limits

## Example Questions

### Example Question #4 : Graphing Polar Form

Draw the curve of  from .

Explanation:

Taking the graph of , we only want the areas in the positive first quadrant because the radius is squared and cannot be negative.

This leaves us with the areas from  to  and  to

Then, when we take the square root of the radius, we get both a positive and negative answer with a maximum and minimum radius of .

To draw the graph, the radius is 0 at  and traces to 1 at . As well, the negative part of the radius starts at 0 and traces to-1 in the opposite quadrant, the third quadrant.

From  to , the curves are traced from 1 to 0 and -1 to 0 in the third quadrant.

Following this pattern, the graph is redrawn again from the areas included in  to .

### Example Question #11 : Functions, Graphs, And Limits

Rewrite in polar form:

Explanation:

### 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.

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### Example Question #1 : Polar Form

What is the equation  in polar form?

Explanation:

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

. Dividing both sides by ,

### Example Question #1 : Polar Form

What is the equation  in polar form?

None of the above

Explanation:

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

### Example Question #1 : Polar Form

Convert the following function into polar form:

Explanation:

The following formulas were used to convert the function from polar to Cartestian coordinates:

Note that the last formula is a manipulation of a trignometric identity.

Simply replace these with x and y in the original function.

### Example Question #1 : Polar Form

What is the equation  in polar form?

Explanation:

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

Dividing both sides by , we get:

### Example Question #20 : Polar

What is the polar form of ?

Explanation:

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

Dividing both sides by , we get:

### Example Question #181 : Parametric, Polar, And Vector

What is the polar form of ?

None of the above

Explanation:

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

### Example Question #23 : Polar

What is the polar form of ?

None of the above

Explanation:

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

Dividing both sides by , we get: