Math Problem Statement
Rewrite the curve
Solution
To rewrite the curve in polar coordinates, we can use the relationships and .
Starting with the given equation:
Substituting the polar coordinates:
This simplifies to:
Using the Pythagorean identity , we have:
Dividing both sides by (assuming ) gives:
Thus, the curve in polar coordinates is:
Would you like to explore more about this curve or have any questions? Here are some related questions you might find interesting:
- What does the graph of look like?
- How do you derive polar coordinates from Cartesian coordinates generally?
- What is the significance of the curve being a circle?
- How does this curve behave as varies?
- Can you convert other conic sections to polar coordinates?
Tip: Always check the domain of when working with polar equations!
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Math Problem Analysis
Mathematical Concepts
Polar Coordinates
Analytic Geometry
Formulas
x = r cos(θ)
y = r sin(θ)
Pythagorean identity: cos²(θ) + sin²(θ) = 1
Theorems
Conversion from Cartesian to Polar Coordinates
Suitable Grade Level
Grades 10-12