Calculus 3 : Cylindrical Coordinates

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #51 : 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:

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 #131 : 3 Dimensional Space

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

Possible Answers:

Correct answer:

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 #53 : 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:

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 #54 : 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:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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 #59 : 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:

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?

Possible Answers:

Correct answer:

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 

 

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