Page 41 - Standard Handbook Of Petroleum & Natural Gas Engineering

30 Mathematics

Table 1-1
Angle Reduction to First Quadrant
If 90" < x < 180" 180" < x < 270" 270" x < 360"
sin x = +cos(x - 900) -sin(x - 180O) -cos(x - 270")
cos x = -sin(x - 90") -cos(x - 180') +sin(x - 270")
tan x = -cot(x - 900) +tan(x - 180") -COt(X - 270")
csc x = +sec(x - 90°) -CSC(X - 180") -sec(x - 270")
sec x = -csc(x - 900) -sec(x - 180") +CSC(X - 270")
cot x = -tan(x - 90") +COt(x - 180") -tan(x - 270')

Table 1-2
Trigonometric Function Values by Quadrant
If 0" < x < 90" 90" < x < 180" 180" < x < 270" 270" < x < 360"
sin x +o to +1 +1 to +o -0 to -1 -1 to -0
cos x +1 to +o -0 to -1 -1 to -0 +o to +1
tan x +o to +- -- to -0 +o to +- -- to -0
csc x +- to +1 +1 to +- -1 to -- -1 to -m
-- to -1
-- to -1
see x +1 to +- -0 to -- -0 to --
+- to +1
cot x +- to +o +- to +o

Table 1-3
Trigonometric Function Values at Major Angle Values

Values at 30" 45" 60"
sin x 112 112 v5 112 6
cos x 112 & 112 v5 112
tan x 113 & 1 &
csc x 2 213 6
sec x 213 & 2
cot x 6 1 113 &

Table 1-4
Relations Between Trigonometric Functions of Angles
Single Angle
sin'x + cos2x = 1
tan x = (sin x)/(cos x)
cot x = l/(tan x)