{Trigonometrical curve}, a curve one of whose co["o]rdinates
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}.
Note: Co["o]rdinates 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
co["o]rdinate 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 co["o]rdinate axes, AX, AY, AZ, and measured
from the corresponding co["o]rdinate 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.
{Cartesian co["o]rdinates}. See under {Cartesian}.
{Geographical co["o]rdinates}, 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 co["o]rdinate.
{Polar co["o]rdinates}, co["o]rdinates 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 co["o]rdinates}, co["o]rdinates the axes of
which intersect at right angles.
{Rectilinear co["o]rdinates}, co["o]rdinates made up of right
lines. Those defined in
(a) and
(c) above are called also {Cartesian co["o]rdinates}.
{Trigonometrical} or {Spherical co["o]rdinates}, 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 co["o]rdinates}, co["o]rdinates 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.