How do you evaluate $cos^-1(sin((5pi)/6))$ without a calculator?

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Answer 1 · 2016-09-15T09:44:31

$cos^(-1)(sin((5pi)/6))=pi/3$

We know that $sin(pi/2+theta)=costheta$

Hence $sin((5pi)/6)=sin((3pi+2pi)/6)=sin((3pi)/6+(2pi)/6)$

= $sin(pi/2+pi/3)=cos(pi/3)=1/2$

Hence $cos^(-1)(sin((5pi)/6))=cos^(-1)(1/2)=pi/3$

How do you evaluate cos^-1(sin((5pi)/6))cos^-1(sin((5pi)/6)) without a calculator?