### All Calculus 2 Resources

## Example Questions

### Example Question #1 : Parametric

Rewrite as a Cartesian equation:

**Possible Answers:**

**Correct answer:**

So

or

We are restricting to values on , so is nonnegative; we choose

.

Also,

So

or

We are restricting to values on , so is nonpositive; we choose

or equivalently,

to make nonpositive.

Then,

and

### Example Question #1 : Parametric, Polar, And Vector

Write in Cartesian form:

**Possible Answers:**

**Correct answer:**

Rewrite using the double-angle formula:

Then

which is the correct choice.

### Example Question #1 : Parametric

Write in Cartesian form:

**Possible Answers:**

**Correct answer:**

, so

.

, so

### Example Question #1 : Parametric, Polar, And Vector

Write in Cartesian form:

**Possible Answers:**

**Correct answer:**

,

so the Cartesian equation is

.

### Example Question #1 : Parametric

Write in Cartesian form:

**Possible Answers:**

**Correct answer:**

so

Therefore the Cartesian equation is .

### Example Question #2 : Parametric, Polar, And Vector Functions

Rewrite as a Cartesian equation:

**Possible Answers:**

**Correct answer:**

, so

This makes the Cartesian equation

.

### Example Question #5 : Parametric, Polar, And Vector

and . What is in terms of (rectangular form)?

**Possible Answers:**

**Correct answer:**

In order to solve this, we must isolate in both equations.

and

.

Now we can set the right side of those two equations equal to each other since they both equal .

.

By multiplying both sides by , we get , which is our equation in rectangular form.

### Example Question #3 : Parametric, Polar, And Vector Functions

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

**Possible Answers:**

**Correct answer:**

Given and , we can find in terms of by isolating in both equations:

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

### Example Question #6 : Parametric, Polar, And Vector

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

**Possible Answers:**

None of the above

**Correct answer:**

In order to find with respect to , we first isolate in both equations:

Since both equations equal , we can then set them equal to each other and solve for :

### Example Question #7 : Parametric, Polar, And Vector

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

**Possible Answers:**

None of the above

**Correct answer:**

In order to find with respect to , we first isolate in both equations:

Since both equations equal , we can then set them equal to each other and solve for :