How do you calculate tan ^-1 (-1/2)tan−1(−12)?

1 Answer
Salvatore I.
Nov 27, 2016

tan^(-1)(-1/2)=-1/2+1/(24)-1/(160)=-0.465tan−1(−12)=−12+124−1160=−0.465
rounded to the third decimal figure

Explanation:

the Mac-laurin expansion is

tan^(-1)(x)=x-x^3/3+x^5/5+o(x^6)tan−1(x)=x−x33+x55+o(x6)

by replacing x=-1/2x=−12 and taking only the first three expansion's terms we get

tan^(-1)(-1/2)=-1/2+1/(3*2^3)-1/(5*2^5)=-0.46456.... that rounded up to the third decimal figure becomes -0.465

indeed tan(-0.465)=-0.502 rounded to the third decimal figure

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