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11.7

  1. Convert the point from cylindrical coordinates to rectangular coordinates.

    (8, −π/4, 4)
    (4Image Upload 2, -4Image Upload 4, 4)
  2. How do you convert polar units to rectangle?
    • x = rcos(theta)
    • y = rsin(theta)
    • z=z
  3. Which octant is (-2, pi/4, 3) in?
    3
  4. Which octant is (-2, pi/6, -8) in?
    7
  5. Convert the point from rectangular coordinates to cylindrical coordinates.

    (5, −5, 2)
    (10/Image Upload 6 , -pi/4 , 2)
  6. How do you change from rectangular units to polar?
    • r2 = x2 + y2
    • tan(Image Upload 8) = y / x
    • z = z
  7. What is (-2, pi/4, 3) in rectangular units?
    (-Image Upload 10 , -Image Upload 12 , 3)
  8. What is (-1 , -5pi/4 , -2) in rectangular units?
    ( Image Upload 14, -Image Upload 16, -2 )
  9. What is (-1 , -Image Upload 18 , 4) in polar units?
    (2, 4pi/3, 4)
  10. Convert the point from rectangular coordinates to cylindrical coordinates.

    (5Image Upload 20, −5, 8)
    (10, -pi/6, 8 )
  11. Find an equation in cylindrical coordinates for the equation given in rectangular coordinates.

    z = x2 + y2 − 6
    z = r2 -6
  12. Find an equation in cylindrical coordinates for the equation given in rectangular coordinates

    x2 + y2 + z2 − 3z = 0
    r2 + z2 − 3z = 0
  13. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

    r = 2
    x2 + y2 = 4
  14. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

    θ = π/3
    xImage Upload 22 - y = 0
  15. Find an equation in rectangular coordinates for the equation given in cylindrical coordinates.

    r = 10 sin(θ)
    x2 + (y-5)2 = 25
  16. How do you convert from rectangular coordinates to spherical?
    • p2 = x2 + y2 + z2
    • tan(Image Upload 24) = y/x
    • Image Upload 26 = arccos(z/Image Upload 28)
  17. How do you convert from spherical coordinates to rectangular?
    • x = Image Upload 30sin(Image Upload 32)cos(Image Upload 34)
    • y = Image Upload 36sin(Image Upload 38)sin(Image Upload 40)
    • z = Image Upload 42cos(Image Upload 44)
  18. Convert the point from rectangular coordinates to spherical coordinates.

    (2, 0, 0)
    (2,0,pi/2)
  19. Convert the point from spherical coordinates to rectangular coordinates.

    (10, π/6, π/4)
    ( Image Upload 46, Image Upload 48 , Image Upload 50 )
  20. Convert the point from spherical coordinates to rectangular coordinates.

    (8, π, π/2)
    (-8,0,0)
  21. Find an equation in rectangular coordinates for the equation given in spherical coordinates.

    ρ = 2
    x2 + y2 + z2 = 4
  22. Find an equation in rectangular coordinates for the equation given in spherical coordinates.

    θ = π4
    x - y = 0
  23. Convert the point from cylindrical coordinates to spherical coordinates.

    (7, π/3, 0)
    (7, pi/3, pi/2)
  24. Convert the point from spherical coordinates to cylindrical coordinates.

    (20, π/3, π/3)
    ( Image Upload 52 , pi/3, 10)
  25. Convert the rectangular equation to an equation in cylindrical coordinates and spherical coordinates.

    x2 + y2 + z2 = 36
    • r2 + z2 =36
    • Image Upload 54 = 6
  26. Find an equation in rectangular coordinates for the equation given in spherical coordinates.

    φ = π6
    z2 = 3(x2 + y2)
Author
NateGatsby
ID
202111
Card Set
11.7
Description
calc1
Updated

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