Page 40 - Standard Handbook Of Petroleum & Natural Gas Engineering

Trigonometry 29
Trigonometric Properties

For any angle 8 as in Figure 1-28

sin 0 = opposite side/hypotenuse = s,/h
cos 0 = adjacent side/hypotenuse = sJh
tan 8 = opposite side/adjacent side = sI/s2 = sin 8/cos 8

and the reciprocals of the basic functions (where the function # 0)

cotangent 8 = cot 8 = l/tan 8 = SJS,
secant 0 = sec 8 = l/cos 8 = h/s2
cosecant 8 = csc 8 = l/sin 8 = h/s,

The functions versed sine, coversed sine, and exterior secant are defined as
vers 0 = 1 - cos 8

covers 8 = 1 - sin 8
exsec 0 = sec 0 - 1

To reduce an angle to the first quadrant of the unit circle, that is, to a degree
measure between 0" and 90", see Table 1-1. For function values at major angle
values, see Tables 1-2 and 1-3. Relations between functions and the sum/
difference of two functions are given in Table 1-4. Generally, there will be two
angles between 0" and 360" that correspond to the value of a function.

Figure 1-28. Trigonometric functions of angles.
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