Page 39 - Standard Handbook Of Petroleum & Natural Gas Engineering

28 Mathematics

-4
A directe angle may be thought of as an amount of rotation rather than a
figure. If A is considered the initial PO ition of the ray, which is then rotated
about its end point A to form <BAB', A 3 ' is its terminal position.
Basic Trigonometric Functions
A trigonometric function of a real number, i.e., a, b, . . ., is the same function
as that of the corresponding directed angle, <A, etc., that is,
a = degree measure of <A

The basic trigonometric functions are the sine, cosine, and tangent.
Given the triangle in Figure 1-27
sine <A = sin a' = a/r

cosine <A = cos aQ = b/r
tangent <A = tan a' = a/b

Radian Measure
From the properties of arcs of circles, if an arc has degree measure m and
radius r, its length L is

L = m/lSO 5cr
therefore

L/r = mn/180
The value L/r is the radian measure of the arc and therefore of its central angle
8, so that

radian measure = degree measure n/180

Figure 1-27. Trigonometric functions of real numbers.