How do you express sin(π4)sin(11π12) without using products of trigonometric functions?

1 Answer
Apr 9, 2016

(22)sin(π12)

Explanation:

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