Use a linear approximation (or differentials) to estimate the given number: tan(47)º

Answer 1

Hi,

first, make a function f(x) = tan(x)

second, f'(x) = sec^2 x

Third, find slope at 45 degree -------> f'(45) = sec^2 x = 2

47 convert to radian ======> you know D/180 = R/Π =======> 47/180 = R/ Π =====> R = 47Π/180

Forth, L = f(45) + m( x - 45) that must convert to radian 45 = Π/4

L = 1 + 2 ( x - Π/4 )

f(47) = L(47) = L(47Π/180 ) = 1 + 2 ( 47Π/180 - Π/4 ) = 1.0698 ≈ 1.07

I hope it is useful,

Minoo