How do you express sin(pi/ 4 ) * sin( ( 11 pi) / 12 ) sin(π4)sin(11π12) without using products of trigonometric functions?

1 Answer
Apr 9, 2016

(-sqrt2/2)sin (pi/12)(22)sin(π12)

Explanation:

P = sin (pi/4).sin (pi/12)P=sin(π4).sin(π12)
Trig table --> sin (pi/4) = sqrt2/2sin(π4)=22
Trig table, trig unit circle, and property of supplement arcs -->
sin ((11pi)/12) = sin (-pi/12 + (12pi)/12) = sin (-pi/12 + pi) = sin(11π12)=sin(π12+12π12)=sin(π12+π)=
= - sin (pi/12).=sin(π12).
The product can be expressed as:
P = - (sqrt2/2)sin (pi/12)P=(22)sin(π12)
If required, you can find P's value by evaluating sin (pi/12)sin(π12), using the trig identity: cos (pi/6) = 1 - 2sin^2 (pi/12) = sqrt3/2cos(π6)=12sin2(π12)=32