Provide the value of arccos(sin(14π/13)) without the use of a calculator
using
cos(π2−θ)=sin(θ)cos(\frac{\pi}{2}-\theta)=sin(\theta)cos(2π−θ)=sin(θ)
arc cos(sin(14π13))arc \space cos (sin(\frac{14\pi}{13}))arc cos(sin(1314π))
arc cos(sin(14π13))=arc cos(cos(π2−14π13))arc\space cos (sin(\frac{14\pi}{13}))=arc\space cos(cos(\frac{\pi}{2}-\frac{14\pi}{13}))arc cos(sin(1314π))=arc cos(cos(2π−1314π))
=arc cos(cos(13π−28π26))=arc\space cos(cos(\frac{13\pi-28\pi}{26}))=arc cos(cos(2613π−28π))
=arc cos(cos(−15π26))=arc\space cos (cos(\frac{-15\pi}{26}))=arc cos(cos(26−15π))
=arc cos(cos(15π26))=arc\space cos(cos(\frac{15\pi}{26}))=arc cos(cos(2615π))
=15π26=\frac{15\pi}{26}=2615π
=1.81245=1.81245=1.81245
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments