The graphs of the elementary functions
      Transcendental functions - The graphs of transcendental functions
     --  Trigonometric (cyclometric) functions and inverse trigonometric functions (arc functions)
         The graphs of the trigonometric functions and inverse trigonometric functions or arc-functions
         The graph of the tangent function and the cotangent function
         The graph of the arc-tangent function and the arc-cotangent function
The graph of the tangent function and the cotangent function
  -  The arc-tangent function  y = tan-1x or  y = arctan x is the inverse of the tangent function, so that its value for any argument is an arc (angle) whose tangent equals the given argument.
That is,  y = tan-1x if and only if  x = tan y.  For example,
Thus, the arc-tangent function is defined for all real arguments, and its principal values are by convention taken to be those strictly between -p/2 and p/2.
  -  The arc-cotangent function  y = cot-1x or  y = arccot x is the inverse of the cotangent function, so that its value for any argument is an arc (angle) whose cotangent equals the given argument.
That is,  y = cot-1x if and only if  x = cot y.  For example,
Thus, the arc-cotangent function is defined for all real arguments, and its principal values are by convention taken to be those strictly between 0 and p.
The graph of the arc-tangent function and the arc-cotangent function
Calculus contents A
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