preface to fifteenth edition

GENERAL INFORMATION, CONVERSION TABLES, AND MATHEMATICS 2.113
V (spherical sector) 2⁄3R2h 1⁄6D2
1 h1
V (spherical segment of one base) 1⁄6h (3r2 h
2
3 3 3)
1 2 2 2
V (spherical segment of two bases) ⁄6h 2(3r3 3r2 h 2)
A (lune) 2R2
where is angle
in radians of lune
Ellipsoid. V 4⁄3abc,
of the semiaxes.
Torus (Fig. 2.7)
where a, b, and c are the lengths
2 2
V 2 Rr
2
Area of surface S 4 Rr
FIGURE 2.6
2.2.3 Trigonometric Functions of an Angle
Let x be any angle whose initial side lies on the positive x axis and
whose vertex is at the origin, and (x, y) be any point on the terminal
side of the angle. (x is positive if measured along OX to the right, from
the y axis; and negative, if measured along OX to the left from the y
axis. Likewise, y is positive if measured parallel to OY, and negative
if measured parallel to OY.) Let r be the positive distance from the
origin to the point. The trigonometric functions of an angle are defined
as follows:
FIGURE 2.7
sine sin r
x
y
cosine cos r
y
FIGURE 2.8
tangent tan x
x
cotangent ctn
cot y
r
secant sec x
r
cosecant x csc y
exsecant x exsec sec 1
versine vers 1 cos
coversine covers
haversine hav
1 sin
1⁄2 vers