Math Problem Statement
Solution
To convert the equation into polar form, we use the relationships between Cartesian coordinates and polar coordinates , which are:
Step-by-Step Conversion:
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Start with the original equation:
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Substitute and :
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Factor out :
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Solve for :
Thus, the polar form of the equation is:
Would you like further explanation on how the polar form was derived, or do you have any other questions?
Related Questions:
- How do you convert any general Cartesian equation to polar form?
- What is the significance of the polar coordinate system in mathematics?
- How does the polar coordinate system simplify equations of circles or lines?
- Can you show how polar and Cartesian coordinates relate geometrically?
- What are common applications of polar coordinates in physics?
Tip: In polar coordinates, the angle represents the direction of the point from the origin, while represents the distance from the origin. This system is useful when analyzing problems with rotational symmetry.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Polar Coordinates
Formulas
x = r * cos(θ)
y = r * sin(θ)
r = -6 / (cos(θ) + 3sin(θ))
Theorems
Conversion from Cartesian to Polar Coordinates
Suitable Grade Level
Grades 10-12