| slovo | definícia |
trigonometrical
(encz) | trigonometrical,trigonometrický adj: Zdeněk Brož |
Trigonometrical
(gcide) | 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] |
| | podobné slovo | definícia |
trigonometrical
(encz) | trigonometrical,trigonometrický adj: Zdeněk Brož |
Inverse trigonometrical functions
(gcide) | 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 |
Trigonometrical coordinates
(gcide) | Coordinate \Co*["o]r"di*nate\, n.
1. A thing of the same rank with another thing; one two or
more persons or things of equal rank, authority, or
importance.
[1913 Webster]
It has neither coordinate nor analogon; it is
absolutely one. --Coleridge.
[1913 Webster]
2. pl. (Math.) Lines, or other elements of reference, by
means of which the position of any point, as of a curve,
is defined with respect to certain fixed lines, or planes,
called coordinate axes and coordinate planes. See
Abscissa.
Note: Coordinates are of several kinds, consisting in some of
the different cases, of the following elements, namely:
(a) (Geom. of Two Dimensions) The abscissa and ordinate of
any point, taken together; as the abscissa PY and
ordinate PX of the point P (Fig. 2, referred to the
coordinate axes AY and AX.
(b) Any radius vector PA (Fig. 1), together with its angle
of inclination to a fixed line, APX, by which any
point A in the same plane is referred to that fixed
line, and a fixed point in it, called the pole, P.
(c) (Geom. of Three Dimensions) Any three lines, or
distances, PB, PC, PD (Fig. 3), taken parallel to
three coordinate axes, AX, AY, AZ, and measured from
the corresponding coordinate fixed planes, YAZ, XAZ,
XAY, to any point in space, P, whose position is
thereby determined with respect to these planes and
axes.
(d) A radius vector, the angle which it makes with a fixed
plane, and the angle which its projection on the plane
makes with a fixed line line in the plane, by which
means any point in space at the free extremity of the
radius vector is referred to that fixed plane and
fixed line, and a fixed point in that line, the pole
of the radius vector.
[1913 Webster]
Cartesian coordinates. See under Cartesian.
Geographical coordinates, the latitude and longitude of a
place, by which its relative situation on the globe is
known. The height of the above the sea level constitutes a
third coordinate.
Polar coordinates, coordinates made up of a radius vector
and its angle of inclination to another line, or a line
and plane; as those defined in
(b) and
(d) above.
Rectangular coordinates, coordinates the axes of which
intersect at right angles.
Rectilinear coordinates, coordinates made up of right
lines. Those defined in
(a) and
(c) above are called also Cartesian coordinates.
Trigonometrical coordinates or Spherical coordinates,
elements of reference, by means of which the position of a
point on the surface of a sphere may be determined with
respect to two great circles of the sphere.
Trilinear coordinates, coordinates of a point in a plane,
consisting of the three ratios which the three distances
of the point from three fixed lines have one to another.
[1913 Webster] |
Trigonometrical curve
(gcide) | 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] |
Trigonometrical function
(gcide) | 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.
FunctionTrigonometric \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] |
Trigonometrical lines
(gcide) | 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] |
Trigonometrical survey
(gcide) | Survey \Sur"vey\, n. [Formerly accentuated universally on the
last syllable, and still so accented by many speakers.]
1. The act of surveying; a general view, as from above.
[1913 Webster]
Under his proud survey the city lies. --Sir J.
Denham.
[1913 Webster]
2. A particular view; an examination, especially an official
examination, of all the parts or particulars of a thing,
with a design to ascertain the condition, quantity, or
quality; as, a survey of the stores of a ship; a survey of
roads and bridges; a survey of buildings.
[1913 Webster]
3. The operation of finding the contour, dimensions,
position, or other particulars of, as any part of the
earth's surface, whether land or water; also, a measured
plan and description of any portion of country, or of a
road or line through it.
[1913 Webster]
Survey of dogs. See Court of regard, under Regard.
Trigonometrical survey, a survey of a portion of country by
measuring a single base, and connecting it with various
points in the tract surveyed by a series of triangles, the
angles of which are carefully measured, the relative
positions and distances of all parts being computed from
these data.
[1913 Webster]
Syn: Review; retrospect; examination; prospect.
[1913 Webster]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] |
Trigonometrically
(gcide) | 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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