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]

Out[1]=

You can find the numerical values of mathematical functions to any precision.

In[2]:= N[Log[2], 40]

Out[2]=

This gives a complex number result.

In[3]:= N[ Log[-2] ]

Out[3]=

Mathematica can evaluate logarithms with complex arguments.

In[4]:= N[ Log[2 + 8 I] ]

Out[4]=

The arguments of trigonometric functions are always given in radians.

In[5]:= Sin[Pi/2]

Out[5]=

You can convert from degrees by explicitly multiplying by the constant Degree.

In[6]:= N[ Sin[30 Degree] ]

Out[6]=

Here is a plot of the hyperbolic tangent function. It has a characteristic "sigmoidal" form.

In[7]:= Plot[ Tanh[x], {x, -8, 8} ]

Out[7]=

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 .