2-D Coordinate Systems
Main Concept
The Cartesian coordinate system is the default 2-D coordinate system used by Maple.
Additionally, Maple supports the following 2-D coordinate systems:
bipolar
cardioid
cassinian
elliptic
hyperbolic
invcassinian
invelliptic
logarithmic
logcosh
maxwell
parabolic
polar
rose
tangent
Conversions
The conversions from the various coordinate systems to cartesian (rectangular) coordinates in 2-space
u,v→x,y
are given by:
bipolar (Spiegel)
x=sinhvcoshv−cosu
y=sinucoshv−cosu
x=u2−v22u2+v22
y=uvu2+v22
cartesian
x=u
y=v
cassinian (Cassinian-oval)
x=a2ⅇ2u+2ⅇucosv+1+ⅇucosv+12
y=a2ⅇ2u+2ⅇucosv+1−ⅇucosv−12
x=coshucosv
y=sinhusinv
x=u2+v2+u
y=u2+v2−u
invcassinian (inverse Cassinian-oval)
x=a2ⅇ2u+2ⅇucosv+1+ⅇucosv+12ⅇ2u+2ⅇucosv+1
y=a2ⅇ2u+2ⅇucosv+1−ⅇucosv−12ⅇ2u+2ⅇucosv+1
invelliptic (inverse elliptic)
x=acoshucosvcoshu2−sinv2
y=asinhusinvcoshu2−sinv2
x=alnu2+v2π
y=2aarctanvuπ
logcosh (ln cosh)
x=alncoshu2−sinv2π
y=2aarctantanhutanvπ
x=au+1+ⅇucosvπ
y=av+ⅇusinvπ
x=u22−v22
y=uv
x=ucosv
y=usinv
x=u2+v2+uu2+v2
y=u2+v2−uu2+v2
x=uu2+v2
y=vu2+v2
Explore by choosing from the different functions and coordinate systems. Adjust the sliders to change parameters such as the domain and the linear factor of the selected function.
Function:
sin(x)cos(x)csc(x)sec(x)tan(x)x^2 - 4ln(x)exp(x)
Coordinate System:
bipolarcartesiancardioidcassinianelliptichyperbolicinvcassinianinvellipticlogarithmiclogcoshmaxwellparabolicpolarrosetangent
Lower limit of Domain, x1
Upper limit of Domain, x2
Linear Factor, a
More MathApps
MathApps/Graphing
Download Help Document