All Calculus 3 Resources
Example Questions
Example Question #39 : Cylindrical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in cylindrical coordinates?
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 #40 : Cylindrical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in cylindrical coordinates?
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 #41 : Cylindrical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in cylindrical coordinates?
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?
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?
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 #122 : 3 Dimensional Space
A point in space is located, in Cartesian coordinates, at . What is the position of this point in cylindrical coordinates?
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 #41 : Cylindrical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in cylindrical coordinates?
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?
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?
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?
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