Can the Polar Form of $y=x^3$ be Plotted on W|A?

In summary, the polar form of y=x^3 is given by r = |x|^3, θ = 3θ, where r is the distance from the origin, θ is the angle with the positive x-axis, and x is the value of the function y=x^3. This is different from the rectangular form, which uses x and y coordinates on a Cartesian plane. The advantages of using polar form for y=x^3 include a more intuitive understanding of the function and simplification of calculations. The polar form can also be converted back to rectangular form using the equations x = rcos(θ) and y = rsin(θ). The graph of y=x^3 in polar form would be a spiral shape
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karush
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MHB
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$y=x^3$ in polar form

I got to this but it didn't plot ${x}^{3}$

$$r=\pm\sqrt{\frac{\sin\left({x}\right)}{\cos^3\left({x}\right)}}$$
 
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Quess I should use W|A for polar plots
 

FAQ: Can the Polar Form of $y=x^3$ be Plotted on W|A?

What is the polar form of y=x^3?

The polar form of y=x^3 is given by r = |x|^3, θ = 3θ, where r is the distance from the origin, θ is the angle with the positive x-axis, and x is the value of the function y=x^3.

How is the polar form of y=x^3 different from the rectangular form?

The polar form of y=x^3 is different from the rectangular form because it represents the same function, but in terms of polar coordinates instead of rectangular coordinates. This means that the values of the function are given in terms of distance and angle from the origin, rather than x and y coordinates on a Cartesian plane.

What are the advantages of using polar form for y=x^3?

One advantage of using polar form for y=x^3 is that it allows for a more intuitive understanding of the function, as the distance from the origin and the angle with the positive x-axis have a clear geometric meaning. Additionally, polar form can simplify certain calculations and make it easier to find patterns and symmetries in the function.

Can the polar form of y=x^3 be converted back to rectangular form?

Yes, the polar form of y=x^3 can be converted back to rectangular form using the equations x = rcos(θ) and y = rsin(θ). This will give the function in terms of x and y coordinates on a Cartesian plane, rather than polar coordinates.

How is the graph of y=x^3 represented in polar form?

The graph of y=x^3 in polar form would be a spiral shape, with the number of revolutions increasing as the distance from the origin increases. The direction of rotation depends on the value of x, with positive values of x resulting in a counter-clockwise rotation and negative values resulting in a clockwise rotation.

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