Functions, Graphs, and Limits

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AP Calculus BC › Functions, Graphs, and Limits

Questions 1 - 10
1

Convert the following cartesian coordinates into polar form:

Explanation

Cartesian coordinates have and , represented as . Polar coordinates have

is the hypotenuse, and is the angle.

Solution:

2

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:

3

What is the vector form of ?

Explanation

Given , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of is

.

4

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given, the vector form is .

So for , we can derive the vector form .

5

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given , the vector form is .

So for , we can derive the vector form .

6

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given, the vector form is .

So for , we can derive the vector form .

7

Given points and , what is the vector form of the distance between the points?

Explanation

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points. That is, for any point and , the distance is the vector .

Subbing in our original points and , we get:

8

Given and , what is in terms of (rectangular form)?

Explanation

Knowing that and , we can isolate in both equations as follows:

Since both of these equations equal , we can set them equal to each other:

9

Given and , what is in terms of (rectangular form)?

None of the answers provided

Explanation

Given and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

10

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:

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