How do you evaluate $arccos(1)$ without a calculator?

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Answer 1 · 2018-04-10T16:33:41

$arccos(1)=0$

We know that,

$color(red)(cos^-1(costheta)=theta, thetain[0,pi]...to(I)$

We have,

$arccos(1)=cos^-1(1)$

But, $color(blue)(cos0=1$

$arccos(1)=color(red)(cos^-1(cos0)$ , where, $color(red)(0 in [0,pi]$

Using $(I),$ we get

$arccos(1)=0$

How do you evaluate arccos(1)arccos(1) without a calculator?