# Calculus 3 : Cylindrical Coordinates

## Example Questions

### Example Question #41 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #42 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #43 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #44 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #45 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #46 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #47 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #48 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #49 : Cylindrical Coordinates

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

Explanation:

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

### Example Question #50 : Cylindrical Coordinates

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

Explanation:

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