How do you evaluate #arctan(2/5)#?

1 Answer
Salvatore I.
Nov 27, 2016

#arctan(2/5) ~=2/5-8/375+32/15625~=0.381# rounded to the third decimal figure

Explanation:

The mac Laurin series for #arctan(x)# is

#arctan(x) = x −x^3/3+x^5/5+ · · · +(−1)^n/(2n+1)x^(2n+1) + o(x^( 2n+2)) #

so #arctan(2/5)=2/5-(2/5)^3/3+(2/5)^5/5+0((2/5)^6)#

#arctan(2/5) ~=2/5-8/375+32/15625~=0.381# rounded to the third decimal figure

Indeed #tan(0.381) ~=0.4=2/5#

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