Question

How do you find the exact value of `cos ((7pi)/12)`?

Answer 1

Exactly `-(sqrt 3-1)/(2sqrt 2) =-0.25882`, nearly

Explanation:

`cos((7pi)/12)`

`=cos(pi/3+pi/4)`

`=cos (pi/3) cos (pi/4) - sin ((pi/3) sin (pi/4)`

`=(1/2)(1/sqrt 2)-(sqrt 3/2)(1/sqrt 2)`

`=-(sqrt 3-1)/(2 sqrt 2)`