General Functions 1 nx 1 1 2 ln1 2 Trigonometric Functions sin 6 cos 2 tan csc x x 6 sec 1 2 cot x x Inverse Trigonometric Functions sin 6 cos 960 tan 3 csc x 1 6 sec 960 x cot 960 Hyperbolic Functions sinh ID: 26314
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ExpansionsforSmallQuantitiesThesetruncatedTaylorseriesexpansionsarevalidforargumentx1. GeneralFunctions (1 x)n1 nx+n(n 1)x2=2 ::: ex1+x+x2=2+::: ln(1+x)x x2=2+::: TrigonometricFunctions sinxx x3=6+::: cosx1 x2=2+::: tanxx+x3=3::: cscx1=x+x=6+::: secx1+x2=2+::: cotx1=x x=3 ::: InverseTrigonometricFunctions sin 1xx+x3=6+::: cos 1x=2 x ::: tan 1xx x3=3+::: csc 1x1=x+1=(6x3)+::: sec 1x=2 1=x ::: cot 1x=2 x+::: HyperbolicFunctions sinhxx+x3=6+::: coshx1+x2=2+::: tanhxx x3=3+::: sechx1 x2=2+::: cschx1=x x=6+::: cothx1=x+x=3+::: InverseHyperbolicFunctions sinh 1xx x3=6+::: cosh 1xln(2x) 1=(4x2) ::: tanh 1xx+x3=3+::: sech 1xln(2=x) x2=4 ::: csch 1x1=x 1=(6x3)+::: coth 1x1=x+1=(3x3)+:::