title: How to solve non-linear system of trigonometric equations in Python (which MATLAB can solve easily)
body: <p>I am trying to solve a system of non-linear trigonometric equations in Python. I tried the following:</p>
  
  <pre><code>from sympy import symbols,solve,sin,cos,pi, Eq
  
  measurements = [(5.71403,0.347064), (4.28889, -0.396854), (5.78091, -7.29133e-05), 
  (2.06098, 0.380579), (8.13321, 0.272391), (8.23589, -0.304111), (6.53473, 0.265354), (1.6023, 
  0.131908)]
  
  f, a, phi = symbols('f a phi')
  eq1 = Eq(a*sin((2.0*pi*f*measurements[0][0])+phi) - measurements[0][1])
  eq2 = Eq(a*sin((2.0*pi*f*measurements[4][0])+phi) - measurements[4][1])
  eq3 = Eq(a*sin((2.0*pi*f*measurements[6][0])+phi) - measurements[6][1])
  solve((eq1,eq2,eq3), (a, f, phi))
  </code></pre>
  
  <p>Python takes forever to attempt to solve the equations. However, MATLAB does it in an instant.</p>
  
  <p>What's the problem?</p>