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Example Questions
Example Question #1 : Cylindrical Coordinates
Convert the following into Cylindrical coordinates.
In order to convert to cylindrical coordinates, we need to recall the conversion equations.
Now lets apply this to our problem.
Example Question #2 : Cylindrical Coordinates
When converting rectangular coordinates to cylindrical coordinates, which variable remains fixed?
None of them are fixed.
To convert a point into cylindrical corrdinates, the transformation equations are
.
Choices for may vary depending on the situation, but the
coordinate remains the same.
Example Question #3 : 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
(Bearing in mind sign convention)
Example Question #1 : 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
(Bearing in mind sign convention)
Example Question #5 : 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
(Bearing in mind sign convention)
Example Question #1751 : Calculus 3
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
(Bearing in mind sign convention)
Example Question #7 : 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
(Bearing in mind sign convention)
Example Question #8 : 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
(Bearing in mind sign convention)
Example Question #9 : 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
(Bearing in mind sign convention)
Example Question #10 : 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
(Bearing in mind sign convention)
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