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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

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6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #29 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(9,30^{\circ},2)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(7.79,4.5,2)

(-7.79,4.5,2)

(-4.5,7.79,2)

(4.5,-7.79,2)

(4.5,7.79,2)

Correct answer:

(7.79,4.5,2)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(9,30^{\circ},2)$

The Cartesian coordinates are

$x=rcos(\theta)\rightarrow7.79$

$y=rsin(\theta)\rightarrow4.5$

$z=z\rightarrow2$

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Example Question #22 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(5,60^{\circ},5)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(-1.52,-4.76,5)

(4.33,2.5,5)

(-4.76,1.52,5)

(2.5,4.33,5)

(-4.76,-1.52,5)

Correct answer:

(2.5,4.33,5)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(5,60^{\circ},5)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow2.5$

$y=rsin(\theta)\rightarrow4.33$

$z=z\rightarrow5$

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Example Question #1781 : Calculus 3

A point in space is located, in cylindrical coordinates, at $(10,-135^{\circ},4)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(-9.96,-0.884,4)

(-0.884,-9.96,4)

(-7.07,-7.07,4)

(7.07,7.07,4)

(-7.07,7.07,4)

Correct answer:

(-7.07,-7.07,4)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(10,-135^{\circ},4)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow-7.07$

$y=rsin(\theta)\rightarrow-7.07$

$z=z\rightarrow4$

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Example Question #32 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(12,120^{\circ},14)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(10.4,-6,14)

(-6,10.4,14)

(6.97,9.77,14)

(-9.77,6.97,14)

(9.77,6.97,14)

Correct answer:

(-6,10.4,14)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(12,120^{\circ},14)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow-6$

$y=rsin(\theta)\rightarrow10.4$

$z=z\rightarrow14$

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Example Question #33 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(15,20^{\circ},11)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(14.1,5.13,11)

(5.13,14.1,11)

(-6.12,-13.7,11)

(6.12,13.7,11)

(13.7,6.12,11)

Correct answer:

(14.1,5.13,11)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(15,20^{\circ},11)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow14.1$

$y=rsin(\theta)\rightarrow5.13$

$z=z\rightarrow11$

Report an Error

Example Question #34 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(20,180^{\circ},5)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(-20,0,5)

(0,-20,5)

(20,0,5)

(0,20,5)

(-12,-16,5)

Correct answer:

(-20,0,5)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(20,180^{\circ},5)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow-20$

$y=rsin(\theta)\rightarrow0$

$z=z\rightarrow5$

Report an Error

Example Question #35 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(4,110^{\circ},6)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(-1.37,3.76,6)

(-0.177,-4,6)

(3.76,-1.37,6)

(1.37,-3.76,6)

(-4,-0.177,6)

Correct answer:

(-1.37,3.76,6)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(4,110^{\circ},6)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow-1.37$

$y=rsin(\theta)\rightarrow3.76$

$z=z\rightarrow6$

Report an Error

Example Question #36 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(8,150^{\circ},8)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(-5.72,5.59,8)

(4,6.93,8)

(4,-6.93,8)

(5.59,-5.72,8)

(-6.93,4,8)

Correct answer:

(-6.93,4,8)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(8,150^{\circ},8)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow-6.93$

$y=rsin(\theta)\rightarrow4$

$z=z\rightarrow8$

Report an Error

Example Question #121 : 3 Dimensional Space

A point in space is located, in cylindrical coordinates, at $(16,145^{\circ},23)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(7.48,14.1,23)

(9.18,-13.1,23)

(-13.1,9.18,23)

(-9.18,-13.1,23)

(14.1,7.48,23)

Correct answer:

(-13.1,9.18,23)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(16,145^{\circ},23)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow-13.1$

$y=rsin(\theta)\rightarrow9.18$

$z=z\rightarrow23$

Report an Error

Example Question #38 : Cylindrical Coordinates

A point in space is located, in cylindrical coordinates, at $(10,-90^{\circ},13)$ . What is the position of this point in Cartesian coordinates?

Possible Answers:

(-8.94,-4.48,13)

(4.48,-8.94,13)

(0,-10,13)

(-4.48,-8.94,13)

(-10,0,13)

Correct answer:

(0,-10,13)

Explanation:

When given cylindrical coordinates of the form $(r,\theta,z)$ and converting to Cartesian coordinates of the form (x,y,z) , the relationship between , , , and $\theta$ will be of use:

$x=rcos(\theta)$

$y=rsin(\theta)$

z=z (This value is identical across Cartesian and cylindrical coordinate systems)

For the cylindrical coordinates $(10,-90^{\circ},13)$

When finding the Cartesian coordinates, be sure if using a calculator to have the correct angle units set (degrees vs radians):

$x=rcos(\theta)\rightarrow0$

$y=rsin(\theta)\rightarrow-10$

$z=z\rightarrow13$

Report an Error

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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #29 : Cylindrical Coordinates

Example Question #22 : Cylindrical Coordinates

Example Question #1781 : Calculus 3

Example Question #32 : Cylindrical Coordinates

Example Question #33 : Cylindrical Coordinates

Example Question #34 : Cylindrical Coordinates

Example Question #35 : Cylindrical Coordinates

Example Question #36 : Cylindrical Coordinates

Example Question #121 : 3 Dimensional Space

Example Question #38 : Cylindrical Coordinates

All Calculus 3 Resources

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