How do you express cos(pi/ 4 ) * sin( ( 15 pi) / 8 ) without using products of trigonometric functions?

1 Answer
Jan 24, 2016

- (sqrt2/2)(sqrt(2 - sqrt2)/2)

Explanation:

Find cos (pi/4) and sin ((15pi)/8) separately
Table for trig functions of Special Arcs gives --> cos (pi/4) = sqrt2/2.

sin ((15pi/8) = sin (-pi/8 + 2pi) = -sin (pi/8).
Find sin (pi/8)
Use trig identity: cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8)
2sin^2 (pi/8) = 1 - sqrt2/2 = (2 - sqrt2)/2
sin (pi/8) = sqrt(2 - sqrt2)/2 (pi/8 is in Quadrant I)
Finally
cos (pi/4).sin( (15pi)/8) = (sqrt2/2)(-sin (pi/8)) =*
= - ((sqrt2)/2)(sqrt(2 - sqrt2)/2)