# Calculus 2 : Parametric

## Example Questions

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

Rewrite as a Cartesian equation:

Explanation:

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 #2 : Parametric, Polar, And Vector

Write in Cartesian form:

Explanation:

Rewrite  using the double-angle formula:

Then

which is the correct choice.

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

Write in Cartesian form:

Explanation:

, so

.

, so

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

Write in Cartesian form:

Explanation:

,

so the Cartesian equation is

.

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

Write in Cartesian form:

Explanation:

so

Therefore the Cartesian equation is  .

### Example Question #1 : Functions, Graphs, And Limits

Rewrite as a Cartesian equation:

Explanation:

, so

This makes the Cartesian equation

.

### Example Question #1 : Parametric Form

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

Explanation:

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 #8 : Parametric, Polar, And Vector

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

Explanation:

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 #9 : Parametric, Polar, And Vector

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

None of the above

Explanation:

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 #1 : Parametric, Polar, And Vector

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

None of the above