Calculus 3 : Cylindrical Coordinates

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #71 : 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:

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 :

Quadrants

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 #72 : 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:

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 :

Quadrants

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 #73 : 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:

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 :

Quadrants

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 #74 : 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:

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 :

Quadrants

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 #75 : 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:

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 :

Quadrants

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 #76 : 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:

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 :

Quadrants

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 #77 : 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:

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 :

Quadrants

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 #78 : 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:

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 :

Quadrants

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 #79 : 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:

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 :

Quadrants

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 #80 : 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:

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 :

Quadrants

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 

 

 

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