Answer to Question #190732 in Algebra for OhMoe

Question

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

Answer 1

using

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

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

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

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

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

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

$=\frac{15\pi}{26}$

$=1.81245$