Question

How do you express `sin(pi/ 4 ) * sin( ( 11 pi) / 12 )` without using products of trigonometric functions?

Answer 1

`(-sqrt2/2)sin (pi/12)`

Explanation:

`P = sin (pi/4).sin (pi/12)`
Trig table --> `sin (pi/4) = sqrt2/2`
Trig table, trig unit circle, and property of supplement arcs -->
`sin ((11pi)/12) = sin (-pi/12 + (12pi)/12) = sin (-pi/12 + pi) =`
`= - sin (pi/12).`
The product can be expressed as:
`P = - (sqrt2/2)sin (pi/12)`
If required, you can find P's value by evaluating `sin (pi/12)`, using the trig identity: `cos (pi/6) = 1 - 2sin^2 (pi/12) = sqrt3/2`