Function
Definition of Function
Func´tion Pronunciation: fŭņk´shŭn n. | 1. | The act of executing or performing any duty, office, or calling; performance. | | 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. | | 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. | | 4. | The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession. | | 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 x2, 3x, Log. x, and Sin. x, are all functions of x. | | 6. | (Eccl.) A religious ceremony, esp. one particularly impressive and elaborate. | | 7. | A public or social ceremony or gathering; a festivity or entertainment, esp. one somewhat formal.Calculus of functions | See under Calculus. |
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. |
| v. i. | 1. | To execute or perform a function; to transact one's regular or appointed business. |
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