Question

How do you express `sin(pi/ 8 ) * cos(( ( 4 pi) / 3 )` without using products of trigonometric functions?

Answer 1

`(1/2)sin (pi/8)`

Explanation:

`P = sin (pi/8).cos (4pi)/3`
Trig table --> `cos (4pi)/3 = cos (- pi/3 + pi) = cos (- pi/3) =`
`= cos (pi/3) = 1/2`. Then, P can be expressed as
`P = (1/2)sin (pi/8)`
We can evaluate `sin (pi/8)` by using the trig identity:
`2sin^2 (pi/8) = 1 - cos (pi/4) = 1 - sqrt2/2`