Roots and periodicity of trigonometric functions

[dennis]

Hi,

i am trying to find the roots of trigonometric functions such as sin(x), cos(x), ...

x = Symbol('x')

print( solve(sin(x), x) )

> [0]

Is there a way to get all roots of sin(x)? For example something like this:

> [pi*n]

or

> [0, pi], periodicity 2*pi

[Sergiu Ivanov]

Hello,

You may find this thread on-topic and, hopefully, helpful:

http://groups.google.com/group/sympy/browse_thread/thread/8440752be0ebea7b/f8f753539be410cd

I don't really possess the latest information on this issue, however,
so you may find it useful to wait for the developers to say their
word.

Sergiu

[Aaron Meurer]

For now, there's no easy way to get it. You can get at least some of
the solutions by adding 2*pi*n to the argument of the trig function:

In [5]: solve(sin(x + 2*pi*n), x)
Out[5]: [-2⋅π⋅n]

I don't know an easy way to get pi*n, though (in the general case).
This trick also works for more complicated functions:

In [19]: solve(sin(x + 2*pi*n) - cos(x + 2*pi*n), x)
Out[19]:
⎡π⋅(-8⋅n - 3) π⋅(-8⋅n + 1)⎤
⎢────────────, ────────────⎥
⎣ 4 4 ⎦

Aaron Meurer

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