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

1 Answer
Nghi N.
Apr 9, 2016

(-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

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