Question

How do you express `sin(pi/ 4 ) * sin( ( 9 pi) / 8 )` without using products of trigonometric functions?

Answer 1

`-sqrt2/2sin (pi/8)`

Explanation:

`P = sin (pi/4)sin ((9pi)/8)`
Trig table -->`sin (pi/4) = sqrt2/2`
sin ((9pi)/8) = sin (pi/8 + pi) = -sin (pi/8)
Therefor, the product P can be expressed as:
`P = -(sqrt2/2)sin (pi/8)`
Note.
We can find P, by evaluation `sin (pi/8)`, by using the trig identity:
`cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8)`