Equations cannot be solved by Wolfram Alpha

Questions
,
1

Hello,

I tried this post solve cos(x)*cos(y)+2*x=0,-sin(x)*sin(y)+2*y=0 for x y in Wolfram Alpha in different variations (brackets used / not used, hand over arguments / variables or not) but all of them resulted in this:

alpha.png
alpha.png756×508 51.8 KB

Here’s another run with the same functions.

What’s the reason for that? How can I solve it?

2

Solve sin(y)+2*y=0 for y

yields y=0

Solve -sin(x)*cos(x)*cos(y)+2*x=0,y=0 for x

yields x=0

3

I don’t know about Wolfram Alpha, but Mathematica gives nontrivial complex solutions too, provided we give bounds on the variables:

solY = Solve[Sin[y] + 2 y == 0 &&
    Abs[y] < 6][[2]]
Solve[Abs[x] < 2 &&
   -Sin[x]*Cos[x]*Cos[y] + 2*x == 0 /. solY, x]
4

I’ve got a typo in the equations in the post, but the link is correct.

Matlab returns:
x: -0.45018361129487357303653869676269
y: 0

But I want to check, that I get all solutions. Matlab doesn’t solve trigonometrical equations over R, e.g. sin(x) = 0 returns: x = 0.
Wolfram does it work better, it returns: x = π n and n element Z

I’ve already plotted the equation above and realized that there’s only one solution, but I want to do that precisely.

5

I don’t know why Wolfram Alpha cannot handle this system. Mathematica finds the real solution this way:

ContourPlot[{Cos[x]*Cos[y] + 2*x == 0,
  -Sin[x]*Sin[y] + 2*y == 0},
 {x, -4, 4}, {y, -4, 4}]
Reduce[Cos[x]*Cos[y] + 2*x == 0 &&
  -Sin[x]*Sin[y] + 2*y == 0 &&
  Abs[x] < 2 && Abs[y] < 2,
 {x, y}, Reals]

There are complex solutions too:

Reduce[Cos[x]*Cos[y] + 2*x == 0 &&
  -Sin[x]*Sin[y] + 2*y == 0 &&
  Abs[x] < 2 && Abs[y] < 2,
 {x, y}]
6

Do you know anybody who could me help solving this system whith Wolfram Alpha?
I think the offical help is only for paying customers, right?

Could you please return me the output of mathematica since I’ve no access to it?

7

Sorry about Wolfram Alpha, I have no idea. The complex solutions near the origin are as follows:

In[3]:= NSolve[Cos[x]*Cos[y] + 2*x == 0 &&
  -Sin[x]*Sin[y] + 2*y == 0 &&
  Abs[x] < 2 && Abs[y] < 2,
 {x, y}]

Out[3]= {{x -> -0.450184, y -> 0.}, {x -> 0.914252 - 1.3176 I, 
  y -> -1.36444 + 1.3176 I}, {x -> 0.914252 + 1.3176 I, 
  y -> -1.36444 - 1.3176 I}}

The first solution is real and it looks the same as in Matlab.

8

Thanks

9

This is not a Matlab site, but the Matlab package Chebfun can probably solve your system.

10

With a free account, can you access

Open in Wolfram Cloud ↗