# Calculus 3 : Cylindrical Coordinates

## Example Questions

### Example Question #131 : 3 Dimensional Space

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #132 : 3 Dimensional Space

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #133 : 3 Dimensional Space

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #134 : 3 Dimensional Space

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #55 : Cylindrical Coordinates

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #56 : Cylindrical Coordinates

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #57 : Cylindrical Coordinates

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #58 : Cylindrical Coordinates

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #141 : 3 Dimensional Space

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates

### Example Question #60 : Cylindrical Coordinates

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

Explanation:

If asked to convert cylindrical coordinates of the form  to Cartesian coordinates of the form , it is necessary to relate  and  to the radius, , and the angle, . The relationships are as follows:

Finding  is much simpler; it does not change between Cartesian and cylindrical coordinates:

However, care should be taken when finding  and ; if using a calculator, it is imperative that the correct units (degrees or radians) are specified for the input!

For our coordinates