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12 Cards in this Set
- Front
- Back
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Conversion from cylindrical to Cartesian coordinates |
x= r cos(θ) y= r sin(θ) z=z |
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Relationship between r and x,y |
r= √(x²+y²) |
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Relationship between θ and x,y |
θ= tan⁻¹(y/x) if x>0 and y≥0 θ= π + tan⁻¹(y/x) if x<0 θ= 2π tan⁻¹(y/x) if x>0 and y<0 |
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Boundaries for θ in cylindrical coordinates |
0≤θ≤2π |
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θ if x=0 |
θ= π/2 for y>0 θ= 3π/2 for y<0 |
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θ when x=y=0 |
undefined |
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requirements for r |
r>0 |
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Length of a vector in cylindrical coordinates given (x,y,z) |
p= √(x²+y²+z²) |
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Length of a vector in spherical coordinates given (x,y,z) |
p= √(x²+y²+z²) |
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Conversion from spherical to Cartesian coordinate system (v= xi + yj +zk |
p= √(x²+y²+z²) ∅= cos⁻¹(z/r)
x= p sin(∅) cos(θ) y= p sin(∅) sin(θ) z= p cos(∅) |
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Limits of p and ∅ |
p≥0 0≤∅≤π |
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Finding θ in spherical coordinate system |
Same as cylindrical system rules
θ= tan⁻¹(y/x) if x>0 and y≥0 θ= π + tan⁻¹(y/x) if x<0 θ= 2π tan⁻¹(y/x) if x>0 and y<0 |
