Evaluating Taylor Polynomial to approximate tan 61

[johnq2k7]

Use an appropriate Taylor polynomial of degree 2 to approximate tan 61.

work shown:

tan (x)= sin(x)/cos(x)

sin (x)= x - (x^3)/3!+ (x^5)/5!- ...+ for all x

cos (x)= x- (x^2)/2! + (x^4)/4!-... for all x

since, tan(x)= sin (x)/cos (x)

therefore , an approximation for tan (x)= x+ (x^3)/3 + (2*x^15)/15+... for all |x|< (Pi)/

do i substitute 61*(180/Pi) for x... to find the value... but this expression is greater than degree 2.. how do i solve this?

since there is no 2nd degree expression for any of the tan x terms... need some help here

 

[johnq2k7]

Re: Evaluating Taylor Polynomial at a certain value... NEED HELP

i think i figured it out.. when their referring to degree 2... they mean n=2

therefore it's the expression tan x= x+x^3/3 +2x^15/15 with x= 61/(Pi/180)

therefore tan 61 approx. equals 1.8...


is this correct?