Question

How do you express `cos( (5 pi)/4 ) * cos (( 4 pi) /3 )` without using products of trigonometric functions?

Answer 1

`sqrt2/4`

Explanation:

The trig unit circle, and trig table -->
`cos ((5pi)/4) = cos (pi/4 + (4pi)/4) = cos (pi/4 + pi) =`
`= -cos pi/4 = -sqrt2/2`
`cos ((4pi)/3) = cos (pi/3 + pi) = -cos (pi/3) = - 1/2`
Therefor, the product can be expressed as;
`P = (-sqrt2/2)(-1/2) = sqrt2/4`