# 11.7

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

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

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

z = x+ 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
x - 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() = y/x
•  = arccos(z/)
17. How do you convert from spherical coordinates to rectangular?
• x = sin()cos()
• y = sin()sin()
• z = cos()
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)
,  )
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)
, pi/3, 10)
25. Convert the rectangular equation to an equation in cylindrical coordinates and spherical coordinates.

x2 + y2 + z2 = 36
• r2 + z2 =36
•  = 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 Updated: 2013-02-20 21:46:07 Tags: calc1 Folders: Description: calc1 Show Answers: