Question

How do you evaluate `cos ((11pi)/8)` using the half angle formula?

Answer 1

First lets convert radian measure into degrees.
`(11*pi)/8=110` degrees (its not mandatory ,but i feel comfortable in degrees than to solve in radians,so i converted.)

Explanation:

`cos(110)`
`impliescos(90+30)`
`impliescos90cos30-sin90sin30` (Applying the identity of cos(a+b))
`implies(1*sqrt(3)/2)-(0*1/2)`
`impliescos(110)=sqrt(3)/2`
`or`
`impliescos((11*pi)/8)=sqrt(3)/2`