Studied by 17 people

5.0(1)

Get a hint

Hint

1

Ellipsoid

All squared, all positive, equals 1

New cards

2

Hyperboloid of One Sheet

All squared, ONE negative, equals 1 (on negative’s axis)

New cards

3

Hyperboloid of Two Sheets

All squared, TWO negatives, equals 1

New cards

4

Elliptic Cone

All squared, ONE negative, equals zero

New cards

5

Elliptic Paraboloid

TWO squared, all positive, equals non-squared variable

New cards

6

Hyperbolic Paraboloid

TWO squared, ONE squared negative, equal to non-squared variable

New cards

7

Rectangular/Cartesian coordinates

(x, y, z)

New cards

8

Cylindrical coordinates

(r, θ, z)

r = radius/distance from origin (xy axis, 2D)

θ = angle

z = height

New cards

9

Spherical coordinates

( p, θ, Φ)

p = distance from origin (3D)

θ = angle

Φ = angle from z-axis

New cards

10

find x (cylindrical to rectangular)

r cosθ

New cards

11

find y (cylindrical to rectangular)

r sinθ

New cards

12

find z (cylindrical or rectangular)

z

New cards

13

find r (rectangular to cylindrical)

sqrt(x² + y²)

New cards

14

find θ (rectangular to cylindrical)

tan^{-1} (y/x)

New cards

15

find x (spherical to rectangular)

p sinΦ cosTHETA

New cards

16

find y (spherical to rectangular)

p sinΦ sinTHETA

New cards

17

find z (spherical to rectangular)

p cos Φ

New cards

18

find p (rectangular to spherical)

sqrt (x² + y² + z²)

New cards

19

find Φ (rectangular to spherical)

cos^{-1} (z/ sqrt(x² + y² + z²) )

New cards

20

find p (cylindrical to spherical)

r / sinTHETA

New cards

21

find r (spherical to cylindrical)

p sinΦ

New cards

22

find r (spherical to cylindrical)

p sinΦ

New cards

23

find z (spherical to cylindrical)

p cosΦ

New cards

24

what shape?

p = n

sphere

New cards

25

what shape?

THETA = pi/n

plane orthogonal to xy plane going through origin

New cards

26

what shape?

Φ = pi/n

elliptic cone (half)

New cards

27

what shape?

Φ = +— pi/n

elliptic cone (full)

New cards

28

what shape?

r = n

right circular cylinder (toilet paper roll)

New cards

29

what shape?

z = n

plane parallel to xy plane, up n units

New cards