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Polar Equations Calculator

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Example
Created on 2024-06-20Asked by Camila Ramirez (Solvelet student)
Convert the polar equation r=2cos⁡(θ) r = 2\cos(\theta) to rectangular form.

Solution

To convert the polar equation r=2cos⁡(θ) r = 2\cos(\theta) to rectangular form: 1. Use the conversion formulas: r=x2+y2,x=rcos⁡(θ),y=rsin⁡(θ). r = \sqrt{x^2 + y^2}, \quad x = r \cos(\theta), \quad y = r \sin(\theta). 2. Substitute r=2cos⁡(θ) r = 2\cos(\theta) into the conversion formulas: x2+y2=2cos⁡(θ),x=2cos⁡(θ)cos⁡(θ),y=2cos⁡(θ)sin⁡(θ). \sqrt{x^2 + y^2} = 2\cos(\theta), \quad x = 2\cos(\theta) \cos(\theta), \quad y = 2\cos(\theta) \sin(\theta). 3. Simplify the expressions: x=2cos⁡2(θ),y=2sin⁡(θ)cos⁡(θ). x = 2\cos^2(\theta), \quad y = 2\sin(\theta)\cos(\theta). Therefore, the rectangular form of the polar equation is x=2cos⁡2(θ) x = 2\cos^2(\theta) and y=2sin⁡(θ)cos⁡(θ) y = 2\sin(\theta)\cos(\theta) . Solved on Solvelet with Basic AI Model
Some of the related questions asked by Ella King on Solvelet
1. Graph the polar equation r=2sin⁡(θ) r = 2\sin(\theta) .2. Find the area enclosed by the curve r=1+2cos⁡(θ)r = 1 + 2\cos(\theta) in the interval [0,π][0, \pi].
DefinitionPolar equations are equations that express the relationship between the radial distance r and the angle θ in polar coordinates. They are used to describe curves in the polar coordinate system. Example: The polar equation r=1+cos(θ) represents a limaçon with an inner loop.
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