Question

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

Answer 1

`tan^(-1)(-1/2)=-1/2+1/(24)-1/(160)=-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)`

by replacing `x=-1/2` 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