Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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Example Question #1 : Parametric Form

Rewrite as a Cartesian equation:

Possible Answers:

Correct answer:

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 #1 : Parametric, Polar, And Vector

Write in Cartesian form:

Possible Answers:

Correct answer:

Explanation:

Rewrite  using the double-angle formula:

Then 

which is the correct choice.

Example Question #1 : Parametric, Polar, And Vector

Write in Cartesian form:

Possible Answers:

Correct answer:

Explanation:

, so 

.

 

, so

Example Question #1 : Parametric, Polar, And Vector

Write in Cartesian form:

Possible Answers:

Correct answer:

Explanation:

,

so the Cartesian equation is 

.

Example Question #1 : Parametric, Polar, And Vector

Write in Cartesian form:

Possible Answers:

Correct answer:

Explanation:

so 

 

Therefore the Cartesian equation is  .

Example Question #1 : Functions, Graphs, And Limits

Rewrite as a Cartesian equation:

Possible Answers:

Correct answer:

Explanation:

, so

This makes the Cartesian equation

.

Example Question #5 : Parametric

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

Possible Answers:

Correct answer:

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 #3 : Parametric, Polar, And Vector Functions

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

Possible Answers:

Correct answer:

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 #1 : Parametric, Polar, And Vector

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

Possible Answers:

None of the above

Correct answer:

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 Form

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

Possible Answers:

None of the above

Correct answer:

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 :

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