Convert Rectangular Equation to Polar

Convert a rectangular equation, such as $x + y = 3$, to a polar equation.

When converting a rectangular equation to a polar equation, we are essentially changing the coordinate system from Cartesian (x, y) to polar (r, theta). This process is important in mathematics because it allows us to analyze and graph equations in a different context, which can simplify problems, especially those involving circles or curves that are more naturally described in polar coordinates. To successfully convert an equation, we use the relationships $r^2 = x^2 + y^2$, $x = r \cos(\theta)$, and $y = r \sin(\theta)$. These fundamental relationships help translate the position of a point given in rectangular coordinates to its position in polar coordinates. Learning to move between these two systems enhances our understanding and flexibility when solving problems involving geometry and trigonometry.

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