code: def TR3(rv):
      """Induced formula: example sin(-a) = -sin(a)
  
      Examples
      ========
  
      >>> from sympy.simplify.fu import TR3
      >>> from sympy.abc import x, y
      >>> from sympy import pi
      >>> from sympy import cos
      >>> TR3(cos(y - x*(y - x)))
      cos(x*(x - y) + y)
      >>> cos(pi/2 + x)
      -sin(x)
      >>> cos(30*pi/2 + x)
      -cos(x)
  
      """
      from sympy.simplify.simplify import signsimp
  
      # Negative argument (already automatic for funcs like sin(-x) -> -sin(x)
      # but more complicated expressions can use it, too). Also, trig angles
      # between pi/4 and pi/2 are not reduced to an angle between 0 and pi/4.
      # The following are automatically handled:
      #   Argument of type: pi/2 +/- angle
      #   Argument of type: pi +/- angle
      #   Argument of type : 2k*pi +/- angle
  
      def f(rv):
          if not isinstance(rv, TrigonometricFunction):
              return rv
          rv = rv.func(signsimp(rv.args[0]))
          if not isinstance(rv, TrigonometricFunction):
              return rv
          if (
              (rv.args[0] - S.Pi / 4).is_positive
              is (S.Pi / 2 - rv.args[0]).is_positive
              is True
          ):
              fmap = {
                  cos: sin,
                  sin: cos,
                  tan: cot,
                  cot: tan,
                  sec: csc,
                  csc: sec,
              }
              rv = fmap[type(rv)](S.Pi / 2 - rv.args[0])
          return rv
  
      return bottom_up(rv, f)
  
imports: from collections import defaultdict
  from sympy.core.add import Add
  from sympy.core.expr import Expr
  from sympy.core.exprtools import Factors, gcd_terms, factor_terms
  from sympy.core.function import expand_mul
  from sympy.core.mul import Mul
  from sympy.core.numbers import pi, I
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.sorting import ordered
  from sympy.core.symbol import Dummy
  from sympy.core.sympify import sympify
  from sympy.core.traversal import bottom_up
  from sympy.functions.combinatorial.factorials import binomial
  from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh, coth, sech, csch, HyperbolicFunction
  from sympy.functions.elementary.trigonometric import cos, sin, tan, cot, sec, csc, sqrt, TrigonometricFunction
  from sympy.ntheory.factor_ import perfect_power
  from sympy.polys.polytools import factor
  from sympy.strategies.tree import greedy
  from sympy.strategies.core import identity, debug
  from sympy import SYMPY_DEBUG
label_desc: Use image node_id 5 for calling a global function with example usage: TR3(rv) and returns: bottom_up, rv, rv, rv