### All Calculus 3 Resources

## Example Questions

### Example Question #21 : Cylindrical Coordinates

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

**Possible Answers:**

**Correct answer:**

When given Cartesian coordinates of the form to cylindrical coordinates of the form , the first and third terms are the most straightforward.

Care should be taken, however, when calculating . 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

For our coordinates

(Bearing in mind sign convention)

### Example Question #21 : Cylindrical Coordinates

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

**Possible Answers:**

**Correct answer:**

When given Cartesian coordinates of the form to cylindrical coordinates of the form , the first and third terms are the most straightforward.

Care should be taken, however, when calculating . 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

For our coordinates

(Bearing in mind sign convention)

### Example Question #23 : Cylindrical Coordinates

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

**Possible Answers:**

**Correct answer:**

When given Cartesian coordinates of the form to cylindrical coordinates of the form , the first and third terms are the most straightforward.

Care should be taken, however, when calculating . 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

For our coordinates

(Bearing in mind sign convention)

### Example Question #24 : Cylindrical Coordinates

**Possible Answers:**

**Correct answer:**

Care should be taken, however, when calculating . The formula for it is as follows:

For our coordinates

(Bearing in mind sign convention)

### Example Question #25 : Cylindrical Coordinates

**Possible Answers:**

**Correct answer:**

Care should be taken, however, when calculating . The formula for it is as follows:

For our coordinates

(Bearing in mind sign convention)

### Example Question #1771 : Calculus 3

**Possible Answers:**

**Correct answer:**

Care should be taken, however, when calculating . The formula for it is as follows:

For our coordinates

(Bearing in mind sign convention)

### Example Question #21 : Cylindrical Coordinates

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

**Possible Answers:**

**Correct answer:**

When given cylindrical coordinates of the form and converting to Cartesian coordinates of the form , the relationship between , , , and will be of use:

(This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates

The Cartesian coordinates are

### Example Question #28 : Cylindrical Coordinates

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

**Possible Answers:**

**Correct answer:**

When given cylindrical coordinates of the form and converting to Cartesian coordinates of the form , the relationship between , , , and will be of use:

(This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates

The Cartesian coordinates are

### Example Question #22 : Cylindrical Coordinates

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

**Possible Answers:**

**Correct answer:**

When given cylindrical coordinates of the form and converting to Cartesian coordinates of the form , the relationship between , , , and will be of use:

(This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates

The Cartesian coordinates are

### Example Question #30 : Cylindrical Coordinates

**Possible Answers:**

**Correct answer:**

(This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

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