All Calculus 3 Resources
Example Questions
Example Question #1 : Spherical Coordinates
Convert the following into spherical coordinates.
In order to convert to spherical coordinates , we need to remember the conversion equations.
Now lets apply this to our problem.
Example Question #2 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #3 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #4 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #2011 : Calculus 3
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #6 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #2011 : Calculus 3
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #8 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #1 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
Example Question #10 : Spherical Coordinates
A point in space is located, in Cartesian coordinates, at . What is the position of this point in spherical coordinates?
When given Cartesian coordinates of the form to cylindrical coordinates of the form
, it would be useful to calculate the
term first, as we'll derive
from it.
Next, begin calculating our angles. Care should be taken, however, when calculating them. Beginning with , 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
To calculate , we can make use of our
value. It is found as
, where
For our coordinates
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