An introduction to mathematics, by A. N. Whitehead.

TRIGONOMETRY 183
PM OM
sider the fractions -M and O, which again
are numbers not dependent on the length of
OP, i.e. not dependent on the scale of our
PM
diagrams. Then we define the number
OP
PA
to be the sine of the number PA, and the
OP,
number OM to be the cosine of the number
OP.OM These fractional forms are clumsy to
OP'
AP
print; so let us put u for the fraction P
which represents the magnitude of the angle
PM
AOP, and put v for the fraction PM, and w
OP
for the fraction OM Then u, v, w, are numOP'
bers, and, since we are talking of any angle
AOP, they are variable numbers. But a
correlation exists between their magnitudes,
so that when u (i.e. the angle AOP) is given
the magnitudes of v and w are definitely determined. Hence v and w are functions of the
argument u. We have called v the sine of
u, and w the cosine of u. We wish to adapt
the general functional notation y =f(x) to
these special cases: so in modern mathematics we write " sin " for "f" when we want