Rectangular to polar conversion usually would involve a 2-dimensional quantity. Can you post an image of the full question along with any figure?Quatros said:Homework Statement
I'm suppose to convert Sqrt[12x-2x^2] into a polar equation.
Homework Equations
The Attempt at a Solution
I went from that equation to r(sin(theta)^2 + 2cos(theta)^2)= 12cos(theta), I really don't know where to go from there.
Charles Link said:When you square both sides, you get ## r^2 ##. You can let ## sin^2(\theta)+cos^2(\theta)=1 ##, leaving one ## r^2 cos^2(\theta) ##. ## \\ ## Additional comment=the equation ## y^2=12x-2x^2 ## looks like an ellipse that is translated in the x-direction. In this case, it would only be taking the positive values of ## y ##. ## \\ ## Additional note: Except for simple graphs, polar coordinate expressions can often be somewhat clumsy to work with.
This is incorrect. The relationship is ##y = r\sin(\theta)## and ##x = r\cos(\theta)##, not the other way around, as you have it.Quatros said:I'm a bit confused,
I went from y^2+2x^2 = 12x
then I converted to
r^2cos(theta) ^2- 2r^2sin(theta ) = 12rsin(theta)
Quatros said:r^2(cos(theta)^2-2r^2sin(theta )) = r(12sin(theta)
Charles Link said:## x=r \cos(\theta) ##. You have it reversed.
Can you see that ## sin^2(\theta)+2 cos^2(\theta)=[sin^2(\theta)+cos^2(\theta)]+cos^2(\theta) ##? That should be obvious.Quatros said:r^2(sin(theta)^2-2r^2cos(theta )^2) = r(12cos(theta))
12cos(theta) = (sin(theta)^2 +2cos(theta)^2)r ,
which is where i get stuck.
## 12 \cos(\theta)=r(1+\cos^2(\theta) ) ##. You can then solve for ## r ##.Quatros said:Ohhh, I see then i get 12cos(theta) = 1+ rcos^2(theta), then i just solve for r?
Polar coordinates are a two-dimensional coordinate system used to locate points in a plane. They are represented by a distance (r) from the origin and an angle (θ) from a reference line, typically the positive x-axis.
To convert polar coordinates to Cartesian coordinates, you can use the following equations:
x = r * cos(θ)
y = r * sin(θ)
where r is the distance from the origin and θ is the angle from the reference line.
Yes, both the distance (r) and angle (θ) in polar coordinates can be negative. A negative distance represents a point in the opposite direction from the origin, and a negative angle represents a point in the opposite direction from the reference line.
The range for the angle (θ) in polar coordinates is typically between 0 and 2π (or 0 and 360 degrees). However, depending on the specific application, the range may vary.
Yes, you can convert Cartesian coordinates to polar coordinates using the following equations:
r = √(x^2 + y^2)
θ = arctan(y/x)
where x and y are the coordinates of the point in the Cartesian system.