ParoXsitiC said:Homework Statement
Convert the polar equation:
r = [itex]\frac{2}{ 2\,\sin \left( \theta
\right) -3\,\cos \left( \theta \right)}
[/itex]
to rectangular form
Homework Equations
x^2 + y^2 = r^2
x = r * cos(theta)
y = r * sin(theta)
The Attempt at a Solution
I tried to to use the x = r cos(theta) technique but had issues simiplifying. Then I tried to x^2+y^2 = r^2 but couldn't complete the square or do anything useful with the r.
The formula for converting from polar to rectangular coordinates is:
x = r cosθ
y = r sinθ
Where r is the distance from the origin and θ is the angle formed with the positive x-axis.
Polar coordinates use distance and angle to locate a point in a plane, while rectangular coordinates use x and y coordinates. In polar coordinates, the origin is the center of the coordinate system and angles are measured counterclockwise from the positive x-axis. In rectangular coordinates, the origin is the bottom left corner and x and y values increase as you move to the right and up, respectively.
To convert negative coordinates from polar to rectangular, simply add or subtract 180° from the given angle depending on the quadrant in which the point lies. If the point is in the 2nd or 3rd quadrant, add 180°. If the point is in the 4th quadrant, subtract 180°.
Yes, there are many online calculators and tools available for converting between polar and rectangular coordinates. Some popular options include Desmos, WolframAlpha, and GeoGebra.
Converting from polar to rectangular coordinates is commonly used in mathematics, physics, and engineering to represent and solve problems involving circular motion, vectors, and complex numbers. It is also useful in navigation and mapping, as well as in computer graphics and 3D modeling.