Question

How do you express `cos( (5 pi)/4 ) * cos (( 11 pi) /6 )` without using products of trigonometric functions?

Answer 1

`-sqrt6/4`

Explanation:

Product `P = cos ((5pi)/4).cos ((11pi)/4)`
Trig table and unit circle -->
`cos ((5pi)/4) = cos (pi/4 + pi) = - cos (pi/4) = - sqrt2/2`
`cos ((11pi)/6) = cos (-pi/6 + (12pi)/6) = cos (-pi/6 + 2pi) =`
`cos (-pi/6) = cos (pi/6) = sqrt3/2`
Therefor:
`P = (-sqrt2/2)(sqrt3/2) = - sqrt6/4`