Convert x^3 -y^3 = 6xy into polar equation

Thread starter Seung Tai Kang
Start date Aug 24, 2017
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Convert Polar

In summary, the equation x^3 - y^3 = 6xy can be converted into polar form by using the substitution x = rcos(theta) and y = rsin(theta). After simplifying, the polar equation becomes r^2 = 6cos(theta)sin(theta). This allows us to graph the equation in polar coordinates, with r representing the distance from the origin and theta representing the angle.

Aug 24, 2017

Seung Tai Kang

Homework Statement

Convert x³ -y³ = 6xy into polar equation.

Homework Equations

x=rcosθ
y=rsinθ
x² +y² = r²

The Attempt at a Solution

r³cos³θ - r³sin³θ = 6r²sinθcosθ

r(cos²θ/sinθ - sin²θ/cosθ) = 6

r(cosθcotθ -sinθtanθ) =6
r = 6/(cosθcotθ - sinθtanθ)

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Aug 24, 2017

Charles Link

Homework Helper

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It looks correct to me.

Related to Convert x^3 -y^3 = 6xy into polar equation

1. What is a polar equation?

A polar equation is a mathematical representation of a curve or shape using polar coordinates, which consist of a radial distance from the origin and an angle from the positive x-axis.

2. How do I convert a Cartesian equation into a polar equation?

To convert a Cartesian equation, such as x^3 - y^3 = 6xy, into a polar equation, you can substitute x = r cos(theta) and y = r sin(theta), and then simplify the resulting equation in terms of r and theta.

3. What are the steps for converting x^3 - y^3 = 6xy into a polar equation?

The steps for converting x^3 - y^3 = 6xy into a polar equation are as follows:

Substitute x = r cos(theta) and y = r sin(theta)
Distribute the power of 3 to both terms
Combine like terms and rearrange to get a single term in r
Factor out r to get the final polar equation

4. Can you provide an example of converting x^3 - y^3 = 6xy into a polar equation?

Sure! If we substitute x = r cos(theta) and y = r sin(theta), we get (r cos(theta))^3 - (r sin(theta))^3 = 6(r cos(theta))(r sin(theta)). Simplifying this further, we get r^3 (cos^3(theta) - sin^3(theta)) = 6r^2 sin(theta) cos(theta). Factoring out r, we finally get r = 6 sin(theta) cos(theta) / (cos^3(theta) - sin^3(theta)).

5. How can I graph a polar equation like r = 6 sin(theta) cos(theta) / (cos^3(theta) - sin^3(theta))?

To graph a polar equation, you can plot points by substituting different values for theta and calculating the corresponding r value. You can also use a graphing calculator or online graphing tool to plot the equation. Keep in mind that the resulting graph will be a curve instead of a straight line, as in the case of Cartesian equations.