How do you evaluate $cos^-1(1/2)$ without a calculator?

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Answer 1 · 2017-01-02T10:19:46

$cos^(-1)(-1/2)=120^@$

See from tables relating to trigonometric ratios of special angles ass shown in figure below
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we have $cos120^@=-1/2$ and $cos240^@=-1/2$

However range for $theta=cos^(-1)x$ is $0 < theta < pi$

Hence, $cos^(-1)(-1/2)=120^@$ .

How do you evaluate cos^-1(1/2)cos^-1(1/2) without a calculator?