Plotting cos(x+2)cos(x)-cos(x+1)² Anonymous

Hello.

Why does sage fail to plot this function?

plot(cos(x+2)cos(x)-cos(x+1)cos(x+1),(x,-pi,pi))

Returns

IndexError: index out of bounds

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There are two points to your question: 1)

cos(x+2)*cos(x)-cos(x+1)*cos(x+1)=-sin(1)^2   #i.e. a constant

(Actually one of the experts should kick in and tell us what to do to make sage simplify your expression to that. I am frequently having problems to force sage to simplify even the most trivial expressions. A tutorial on that would be nice...)

2) sage uses matplotlib to do the plotting of your expression. The automatic selection of a 'proper' y-axis extent of that can cause problems when the actual y-extent of your data is identically zero. So, do something like:

plot(cos(x+2)*cos(x)-cos(x+1)*cos(x+1),(-pi,pi),ymin=-sin(1)^2*1.1,ymax=-sin(1)^2*.9)

and you'll get: ... a nice straight line

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For your first point, try f = cos(x+2)*cos(x)-cos(x+1)*cos(x+1) and then f.trig_reduce(). In general, you need "*" to indicate multiplication: replace "cos(x+2) cos(x)" with "cos(x+2) * cos(x)", for example. In this particular example, there seems to be another issue, and it might be a bug. Try replacing "2" with "2.01" and it should plot okay.

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