### All Calculus 3 Resources

## Example Questions

### Example Question #1 : Spherical Coordinates

Convert the following into spherical coordinates.

**Possible Answers:**

**Correct answer:**

In order to convert to spherical coordinates , we need to remember the conversion equations.

Now lets apply this to our problem.

### Example Question #2 : Spherical Coordinates

A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?

**Possible Answers:**

**Correct answer:**

When given Cartesian coordinates of the form to cylindrical coordinates of the form , it would be useful to calculate the term first, as we'll derive from it.

Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , the formula for it is as follows:

However, it is important to be mindful of the signs of both and , bearing in mind which quadrant the point lies; this will determine the value of :

It is something to bear in mind when making a calculation using a calculator; negative values by convention create a negative , while negative values lead to

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #3 : Spherical Coordinates

A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?

**Possible Answers:**

**Correct answer:**

When given Cartesian coordinates of the form to cylindrical coordinates of the form , it would be useful to calculate the term first, as we'll derive from it.

Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , the formula for it is as follows:

However, it is important to be mindful of the signs of both and , bearing in mind which quadrant the point lies; this will determine the value of :

It is something to bear in mind when making a calculation using a calculator; negative values by convention create a negative , while negative values lead to

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #4 : Spherical Coordinates

A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?

**Possible Answers:**

**Correct answer:**

When given Cartesian coordinates of the form to cylindrical coordinates of the form , it would be useful to calculate the term first, as we'll derive from it.

Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , the formula for it is as follows:

However, it is important to be mindful of the signs of both and , bearing in mind which quadrant the point lies; this will determine the value of :

It is something to bear in mind when making a calculation using a calculator; negative values by convention create a negative , while negative values lead to

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #1 : Spherical Coordinates

**Possible Answers:**

**Correct answer:**

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #1 : Spherical Coordinates

**Possible Answers:**

**Correct answer:**

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #7 : Spherical Coordinates

**Possible Answers:**

**Correct answer:**

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #8 : Spherical Coordinates

**Possible Answers:**

**Correct answer:**

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #9 : Spherical Coordinates

**Possible Answers:**

**Correct answer:**

To calculate , we can make use of our value. It is found as

, where

For our coordinates

### Example Question #10 : Spherical Coordinates

**Possible Answers:**

**Correct answer:**

To calculate , we can make use of our value. It is found as

, where

For our coordinates