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# Equation of Curve under Both Cartesian and Polar Coordinates

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r = 10sin(theta) + 10cos(theta)

which one is it ?
circle
ellipse
parabola
line

https://brainmass.com/math/calculus-and-analysis/equation-curve-under-both-cartesian-polar-coordinates-172645

#### Solution Summary

The solution shows the conversion of the equations between Cartesian and polar coordinates.

\$2.19

## Relativity: Differential Geometry

A particle moves along a parametrized curve given by

x(lamda)=cos(lamda), y(lamda)=sin(lamda), z(lamda)=lamda

Express the path of the curve in the spherical polar coordinates {r, theta, pheta}
where x = rsin(theta)cos(pheta)
y=rsin(theta)sin(pheta)
z=rcos(theta)
so that the metric is
ds^2=dr^2+(r^2)d(theta)^2+(r^2)sin^2(theta)d(pheta)^2

Calculate the components of the tangent vector to the curve in both Cartesian and spherical polar coordinate systems.

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