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2 definitions found
 for Trigonometrical function
From The Collaborative International Dictionary of English v.0.48 :

  Function \Func"tion\, n. [L. functio, fr. fungi to perform,
     execute, akin to Skr. bhuj to enjoy, have the use of: cf. F.
     fonction. Cf. Defunct.]
     1. The act of executing or performing any duty, office, or
        calling; performance. "In the function of his public
        calling." --Swift.
        [1913 Webster]
  
     2. (Physiol.) The appropriate action of any special organ or
        part of an animal or vegetable organism; as, the function
        of the heart or the limbs; the function of leaves, sap,
        roots, etc.; life is the sum of the functions of the
        various organs and parts of the body.
        [1913 Webster]
  
     3. The natural or assigned action of any power or faculty, as
        of the soul, or of the intellect; the exertion of an
        energy of some determinate kind.
        [1913 Webster]
  
              As the mind opens, and its functions spread. --Pope.
        [1913 Webster]
  
     4. The course of action which peculiarly pertains to any
        public officer in church or state; the activity
        appropriate to any business or profession.
        [1913 Webster]
  
              Tradesmen . . . going about their functions. --Shak.
        [1913 Webster]
  
              The malady which made him incapable of performing
              his
              regal functions.                      --Macaulay.
        [1913 Webster]
  
     5. (Math.) A quantity so connected with another quantity,
        that if any alteration be made in the latter there will be
        a consequent alteration in the former. Each quantity is
        said to be a function of the other. Thus, the
        circumference of a circle is a function of the diameter.
        If x be a symbol to which different numerical values can
        be assigned, such expressions as x^{2, 3^{x}, Log. x, and
        Sin. x, are all functions of x.
        [1913 Webster]
  
     6. (Eccl.) A religious ceremony, esp. one particularly
        impressive and elaborate.
  
              Every solemn `function' performed with the
              requirements of the liturgy.          --Card.
                                                    Wiseman.
        [Webster 1913 Suppl.]
  
     7. A public or social ceremony or gathering; a festivity or
        entertainment, esp. one somewhat formal.
  
              This function, which is our chief social event. --W.
                                                    D. Howells.
        [Webster 1913 Suppl.]
  
     Algebraic function, a quantity whose connection with the
        variable is expressed by an equation that involves only
        the algebraic operations of addition, subtraction,
        multiplication, division, raising to a given power, and
        extracting a given root; -- opposed to transcendental
        function.
  
     Arbitrary function. See under Arbitrary.
  
     Calculus of functions. See under Calculus.
  
     Carnot's function (Thermo-dynamics), a relation between the
        amount of heat given off by a source of heat, and the work
        which can be done by it. It is approximately equal to the
        mechanical equivalent of the thermal unit divided by the
        number expressing the temperature in degrees of the air
        thermometer, reckoned from its zero of expansion.
  
     Circular functions. See Inverse trigonometrical functions
        (below). -- Continuous function, a quantity that has no
        interruption in the continuity of its real values, as the
        variable changes between any specified limits.
  
     Discontinuous function. See under Discontinuous.
  
     Elliptic functions, a large and important class of
        functions, so called because one of the forms expresses
        the relation of the arc of an ellipse to the straight
        lines connected therewith.
  
     Explicit function, a quantity directly expressed in terms
        of the independently varying quantity; thus, in the
        equations y = 6x^{2, y = 10 -x^{3}, the quantity y is an
        explicit function of x.
  
     Implicit function, a quantity whose relation to the
        variable is expressed indirectly by an equation; thus, y
        in the equation x^{2 + y^{2} = 100 is an implicit
        function of x.
  
     Inverse trigonometrical functions, or Circular functions,
        the lengths of arcs relative to the sines, tangents, etc.
        Thus, AB is the arc whose sine is BD, and (if the length
        of BD is x) is written sin ^{-1x, and so of the other
        lines. See Trigonometrical function (below). Other
        transcendental functions are the exponential functions,
        the elliptic functions, the gamma functions, the theta
        functions, etc.
  
     One-valued function, a quantity that has one, and only one,
        value for each value of the variable. -- Transcendental
     functions, a quantity whose connection with the variable
        cannot be expressed by algebraic operations; thus, y in
        the equation y = 10^{x is a transcendental function of x.
        See Algebraic function (above). -- Trigonometrical
     function, a quantity whose relation to the variable is the
        same as that of a certain straight line drawn in a circle
        whose radius is unity, to the length of a corresponding
        are of the circle. Let AB be an arc in a circle, whose
        radius OA is unity let AC be a quadrant, and let OC, DB,
        and AF be drawnpependicular to OA, and EB and CG parallel
        to OA, and let OB be produced to G and F. E Then BD is the
        sine of the arc AB; OD or EB is the cosine, AF is the
        tangent, CG is the cotangent, OF is the secant OG is the
        cosecant, AD is the versed sine, and CE is the coversed
        sine of the are AB. If the length of AB be represented by
        x (OA being unity) then the lengths of Functions. these
        lines (OA being unity) are the trigonometrical functions
        of x, and are written sin x, cos x, tan x (or tang x), cot
        x, sec x, cosec x, versin x, coversin x. These quantities
        are also considered as functions of the angle BOA.
        Function

From The Collaborative International Dictionary of English v.0.48 :

  Trigonometric \Trig`o*no*met"ric\, Trigonometrical
  \Trig`o*no*met"ric*al\, [Cf. F. trigonom['e]trique.]
     Of or pertaining to trigonometry; performed by the rules of
     trigonometry.
     [1913 Webster] --{Trig`o*no*met"ric*al*ly, adv.
     [1913 Webster]
  
     Trigonometrical curve, a curve one of whose coordinates is
        a trigonometric function of the other.
  
     Trigonometrical function. See under Function.
  
     Trigonometrical lines, lines which are employed in solving
        the different cases of plane and spherical trigonometry,
        as sines, tangents, secants, and the like. These lines, or
        the lengths of them, are trigonometrical functions of the
        arcs and angles to which they belong.
  
     Trigonometrical survey. See under Survey.
        [1913 Webster]

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