Question

How do you find the exact value of cos π/8?

Answer 1

`cos (pi/8) = cos 22.5^o = (1/2)sqrt(2+sqrt 2)=0.923879532`

Explanation:

The value is a surd and cannot be expressed in a closed form of (an

integer)/(an integer). Approximations up to about 10 significant

digits (sd), using 12-sd calculator.

`cos a = sqrt((1 + cos 2a)/2)`

So, `cos(pi/8)=sqrt((1+cos (pi/4))/2)`

`= sqrt((1+1/sqrt 2)/2)=.(1/2)sqrt((2+sqrt 2))=0.923879532`