Question

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

Answer 1

`-sqrt6/4`

Explanation:

`P = sin (pi/4).sin ((4pi)/3)` =
Trig table and unit circle gives -->
`sin(pi/4) = sqrt2/2`, and `sin ((4pi)/3) = - sin (pi/3) = - sqrt3/2`
Therefor -->
`P = (sqrt2/2)(- sqrt3/2) = - sqrt6/4`