Solve trigonometric equation

asked 2016-08-28 23:23:50 +0200

proy
21 ●2 ●3 ●5

How do I solve simple trigonometric equation 2*cot(2x)=0?

I tried solve, but it gives me one solution, I need solution with n.

Thank you.

answered 2016-08-28 23:36:48 +0200

mforets
1413 ●9 ●27 ●44 http://marcelo-forets.fr/

With solve(2*cot(x)==0, x, to_poly_solve = 'force') you will get all solutions, where $\pi z_{xx}$ should be interpreted as a multiple integer of $\pi$.

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It doesn't work for 2*cot(2x). More precisely, solve(2*cot(2*x)==0, x, to_poly_solve='force') returns empty list.

proy ( 2016-08-28 23:40:30 +0200 )edit

Strange. I get $\pi/2 + \pi z$, see here.

mforets ( 2016-08-28 23:52:52 +0200 )edit

Pay attention to argument of cotangent: it is 2x: see here See equation solver for correct answer.

proy ( 2016-08-29 08:34:30 +0200 )edit

Ok! Sorry, I don't know why does it return the empy list. Of course, a change of variables var('x, y') and solve([2*cot(y)==0, y==2*x], x, y, to_poly_solve = 'force') will do the job, but it's awkward..

mforets ( 2016-08-29 10:07:10 +0200 )edit

I agree...

proy ( 2016-08-29 10:20:14 +0200 )edit

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