Schaum's Outline of Theory and Problems of Beginning Calculus

Chapter 28The Tangent andOther Trigonometric FunctionsBesides the sine and cosine functions, there are four other important trigonometric functions, all ofthem expressible in terms of sin x and cos x.sin xDefinitions: Tangent function tan x = -cos xcos x 1Cotangent finctionsin x tan x1Secant firnction secx=- cos x1Cosecantfiurction csc x = -sin xcot x = - - -EXAMPLE Let us calculate, and collect in Table 28-1, some of the values of tan x.sin 0 0cos0 1tan 0 = - = - = 0a sin (n/6) 112 1 1 9 Jstan - = -= - - = - - = -6 cos (46) J3/2 J3 J3 Js 3a sin (n/4) Jz/2=4 cos (d4) fi/2 =1a sin (a/3) =-- J5/23 cos (a/3) 1/2 -8tan - = -tan - = -Notice that tan (42) is not defined, since sin (42) = 1 and cos (n/2) = 0. Moreover,sin xsin xlim tan x = lim -- - +a and lim tanx = lim -- - -00x-qn/2)- x--r(x/2)+ cos x x+n+/2 x-+n+/2 cos xbecause cos x > 0 for x immediately to the left of n/Z and cos x < 0 for x immediately to the right ofn/2.Table 28-1X0It-6a -43tan x0- x 0.5831fi x 1.73214