How does one graph this?

asked 2014-11-24 21:00:32 -0500

Krishnan Arbuja gravatar image

updated 2014-11-25 18:54:59 -0500

I am trying to parametrize $x^2+y^2+sin(4x)+sin(4y)=4$.

I need to find a way of taking the intersections between $x^2+y^2+\sin(4x)+\sin(4y)=4$, and $\tan(nx)$. As n increases from $0\le{n}\le{2\pi}$, I can take the following in coordinate-form....

$$(n,\text{The x-intersection value})$$ $$(n,\text{The y-intersection value})$$

Finally I need to take the following to graph its parametric derivative. Which is...

$$\frac{({\text{The x-intersection value}})^2+4\cos(4(\text{The x-intersection value}))}{-(\text{The y-intersection value})^2-4\cos(4(\text{The y-intersection}))}$$

I have little knowledge with how to use sage. If someone can help I'll be thankful.

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You can try plotting separately and then combine

p1 = implicit_plot(x^2+y^2+sin(4*x)+sin(4*y)==4,(x,-3,3),(y,-3,3), color='red')
p2 = plot(tan(x), (x,-3,3), ymin=-3, ymax=3, color='blue')
SL gravatar imageSL ( 2014-11-26 03:09:07 -0500 )edit