Trigonometry
     Graphs of Trigonometric Functions
     The Graph of the Cotangent Function  f (x) = cotx
      Properties of the cotangent function
         Domain and range
         Zeros of the cotangent function
         Parity and periodicity of the cotangent function
      The cotangent function behavior and monotony
Graphs of trigonometric functions
The graph of the cotangent function  f (x) = cot x
  By associating the values of the cotangent of arcs of the unit circle, to corresponding arcs in a coordinate  system obtained are points P (x, cot x) of the graph of the cotangent function.
The graph of the cotangent function in the down figure is drawn using the relation between tangent and cotangent which states,
cot x = - tan (x + p/2).
Properties of the cotangent function
 - Domain
From the definition, cot x = cos x/sin x, follows that all real numbers x, as input values, associate exactly one functional value as output, except the zeroes of the sine function from the denominator, thus
  Df  = R \ {kpk Z}.
 - Range     f (D) = R  or  - oo < cot x < + oo.
 - Zeros of the cotangent function
The zeroes of the cotangent are determined by the zeroes of the cosine function from the numerator, thus
x = p/2 + kpk Z.
 - Parity and periodicity
The cotangent is an odd function since
The cotangent is periodic function with the period p = p since for every arc x from the domain
cot (x + kp) = cot x.
Behavior of the cotangent function  (monotonicity)
The cotangent is decreasing function in every interval between any of the two successive vertical asymptotes
that is,    f (x1) > f (x2 for all  x1 < x2.
The vertical asymptotes are,   x = kp,   k Z.
Trigonometry contents A
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