Question #190732

Provide the value of arccos(sin(14π/13)) without the use of a calculator


1
Expert's answer
2021-05-10T13:05:10-0400

using

cos(π2θ)=sin(θ)cos(\frac{\pi}{2}-\theta)=sin(\theta)


arc cos(sin(14π13))arc \space cos (sin(\frac{14\pi}{13}))


arc cos(sin(14π13))=arc cos(cos(π214π13))arc\space cos (sin(\frac{14\pi}{13}))=arc\space cos(cos(\frac{\pi}{2}-\frac{14\pi}{13}))


=arc cos(cos(13π28π26))=arc\space cos(cos(\frac{13\pi-28\pi}{26}))


=arc cos(cos(15π26))=arc\space cos (cos(\frac{-15\pi}{26}))


=arc cos(cos(15π26))=arc\space cos(cos(\frac{15\pi}{26}))


=15π26=\frac{15\pi}{26}


=1.81245=1.81245


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