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3.2.6 Elementary Transcendental Functions

Elementary transcendental functions.

  • Mathematica gives exact results for logarithms whenever it can. Here is

  • In[1]:= Log[2, 1024]


  • You can find the numerical values of mathematical functions to any precision.
  • In[2]:= N[Log[2], 40]


  • This gives a complex number result.
  • In[3]:= N[ Log[-2] ]


  • Mathematica can evaluate logarithms with complex arguments.
  • In[4]:= N[ Log[2 + 8 I] ]


  • The arguments of trigonometric functions are always given in radians.
  • In[5]:= Sin[Pi/2]


  • You can convert from degrees by explicitly multiplying by the constant Degree.
  • In[6]:= N[ Sin[30 Degree] ]


  • Here is a plot of the hyperbolic tangent function. It has a characteristic "sigmoidal" form.
  • In[7]:= Plot[ Tanh[x], {x, -8, 8} ]

    There are a number of additional trigonometric and hyperbolic functions that are sometimes used. The versine function is defined as . The haversine is simply . The complex exponential is sometimes written as . The gudermannian function is defined as . The inverse gudermannian is . The gudermannian satisfies such relations as