Bipolarity said:Homework Statement
Express the following equation in Cartesian form
[tex] r = 1 - cos(θ) [/tex]
Homework Equations
[tex] x = r*cos(θ) [/tex]
[tex] y = r*sin(θ) [/tex]
[tex] r^{2} = x^{2} + y^{2} [/tex]
[tex] tan(θ) = \frac{y}{x} [/tex]
The Attempt at a Solution
I have no idea... a hint would be nice thanks!
BiP
gabbagabbahey said:If [itex]x=r\cos\theta[/itex], what is [itex]\cos\theta[/itex]? If [itex]x^2+y^2=r^2[/itex], and [itex]r\geq 0[/itex], what is [itex]r[/itex]?
Polar coordinates use a distance from the origin and an angle to represent a point, while Cartesian coordinates use horizontal and vertical distances from the origin.
To convert a polar equation to a Cartesian equation, use the following substitutions: x = rcosθ and y = rsinθ. Then, simplify the equation using trigonometric identities.
Expressing a polar equation as a Cartesian equation allows for easier graphing and calculation of points in the Cartesian plane.
Yes, all polar equations can be expressed as Cartesian equations using the substitution method mentioned earlier.
The only limitation is that the resulting Cartesian equation may be more complex and difficult to work with compared to the original polar equation.