# Calculus 2 : Parametric, Polar, and Vector

## Example Questions

### Example Question #41 : Parametric Form

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

None of the above

Explanation:

Given   and , let's solve both equations for :

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

### Example Question #42 : Parametric Form

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

None of the above

Explanation:

Given   and , let's solve both equations for :

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

### Example Question #43 : Parametric Form

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

None of the above

Explanation:

Given   and , let's solve both equations for :

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

### Example Question #44 : Parametric Form

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

None of the above

Explanation:

Given  and , let's solve both equations for :

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

### Example Question #41 : Parametric Form

Find   when  and .

Explanation:

If  and , then we can use the chain rule to define  as

.

We use the power rules

and where  is a constant, the constant rule

where   is a constant, and the additive property of derviatives

.

In this case

and

,

therefore

### Example Question #46 : Parametric Form

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

None of the above

Explanation:

Given  and , let's solve both equations for :

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

### Example Question #51 : Parametric Form

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

None of the above

Explanation:

Given  and , let's solve both equations for :

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

### Example Question #52 : Parametric Form

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

Explanation:

Given  and , let's solve both equations for :

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

### Example Question #53 : Parametric Form

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

None of the above

Explanation:

Given  and ,  let's solve both equations for :

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

### Example Question #54 : Parametric Form

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