How do you evaluate $cos^-1 (-1/2)$ ?

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Answer 1 · 2017-06-19T10:05:27

$cos^-1(-1/2) = (2pi)/3$

Note: $cos (pi/3)=1/2 , cos (pi-pi/3)=-1/2$

Let $cos^-1(-1/2) = theta :. cos theta = (-1/2)$ We know

$cos ((2pi)/3)=-1/2 :.cos theta = cos ((2pi)/3) :. theta = (2pi)/3$

Hence $cos^-1(-1/2) = (2pi)/3$

Range of $cos^-1(x)$ is $[0,pi] and (2pi)/3$ is in the range.

So $cos^-1(-1/2) = (2pi)/3$ [Ans]

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