title: How precise is numpy's sin(x) ? How do I find out? [need it to numerically solve x=a*sin(x)]
body: <p>I'm trying to numerically solve the equation <code>x=a*sin(x)</code>, where <code>a</code> is some constant, in python. I already tried first solving the equation symbolically, but it seems this particular shape of expression isn't implemented in sympy. I also tried using sympy.nsolve(), but it only gives me the first solution it encounters. </p>
  
  <p>My plan looks something like this:</p>
  
  <pre><code>x=0
  a=1
  rje=[]
  while(x&lt;a):
      if (x-numpy.sin(x))&lt;=error_sin:
          rje.append(x)
      x+=increment
  
  print(rje)
  </code></pre>
  
  <p>I don't want to waste time or risk missing solutions, so I want to know how to find out how precise numpy's sinus is on my device (that would become error_sin).</p>
  
  <p>edit: I tried making both error_sin and increment equal to the machine epsilon of my device but it a) takes to much time, and b) sin(x) is less precise that x and so I get a lot of non-solutions (or rather repeated solutions because sin(x) grows much slower than x). Hence the question. </p>
  
  <p>edit2: Could you please just help me answer the question about precision of numpy.sin(x)? I provided information about the purpose purely for context. </p>