You didn't include r when substituting for x & y on the right hand side of the equation.steveFerrera said:Homework Statement
(x^2+y^2)^3=2x^2-2y^2
I need to convert this to polar form; anyone have any ideas where to start?
Homework Equations
r^2=x^2+y^2
y=r*sin(theta)
x=r*cos(theta)
tan(theta)=x/y
The Attempt at a Solution
(r^2)^3=2cos^2(theta)-2sin^2(theta)
I know this is incorrect but I'm a bit overwhelmed on this one.
any help would be wonderful! thanks!
Regarding the right hand side:steveFerrera said:r^5=2cos^2(theta)-2sin^2(theta)
did i do the substitutions right on the right side of the equation? or do i need to do some other manipulation of my relevant equations?
The purpose of converting from rectangular to polar coordinates is to represent a point in a two-dimensional plane using polar coordinates, which consist of a distance (r) from the origin and an angle (θ) from the positive x-axis. This representation can be useful in many applications, such as in physics, engineering, and mathematics.
To convert from rectangular to polar coordinates, you can use the following formulas:
r = √(x² + y²)
θ = arctan(y/x)
where x and y are the rectangular coordinates of the point and r and θ are the polar coordinates. It is important to note that the angle (θ) is measured in radians, not degrees.
The relationship between rectangular and polar coordinates is that they both represent the same point in a two-dimensional plane. Rectangular coordinates use the x and y axes to indicate the position of a point, while polar coordinates use the distance from the origin and the angle from the positive x-axis to represent the point.
One of the main advantages of using polar coordinates over rectangular coordinates is that they are often more convenient and efficient for representing points in circular or radial patterns. This is because the distance (r) and angle (θ) in polar coordinates can easily describe a point's position in relation to the origin, whereas rectangular coordinates may require more complex calculations.
Yes, you can convert from polar to rectangular coordinates using the following formulas:
x = r * cos(θ)
y = r * sin(θ)
where x and y are the rectangular coordinates and r and θ are the polar coordinates. This conversion can be useful when you need to plot points in a rectangular coordinate system or perform calculations that require rectangular coordinates.