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21 Cards in this Set
- Front
- Back
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Spherical coordinates
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(ρ, ϴ,ϕ)
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(x,y,z)-->(ρ, ϴ,ϕ)
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p^2=x^2+y^2+z^2
ϴ is the angle from the x-axis to the point ϕ is the angle between the positive z axis and the line seg. |
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(ρ, ϴ,ϕ)-->(x,y,z)
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x=psinϕcosϴ
y=psinϕsinϴ z=pcosϕ |
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p=c
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sphere
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ϴ=c
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vertical half-plane
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ϕ=c
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0<c<pi/2=half-cone above xy
pi/2<c<pi=half-cone below xy c=pi/2=horizontal half-plane |
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ellipsoid
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x^2/a^2+y^2/b^2+z^2/c^2=1
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cone
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z^2=x^2/a^2+y^2/b^2
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elliptic paraboloid
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z/c=x^2/a^2+y^2/b^2
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hyperboloid of one sheet
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x^2/a^2+y^2/b^2--z^2/c^2=1
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hyperboloid of 2 sheets
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-x^2/a^2--y^2/b^2+z^2/c^2=1
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sin^2+cos^2
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1
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tan^2+1
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sec^2
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1+cot^2
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csc^2
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sin(-x)
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-sin(x)
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cos(-x)
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cos(x)
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sin(x+y)
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sin(x)cosy+cosxsiny
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cos(x+y)
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cosxcosy-sinxsiny
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tan(x+y)
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(tanx+tany)/(1-tanxtany)
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sin2x
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2sinxcosx
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cos2x
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2cos^2-1=1-2sin^2=cos^2-sin^2
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