How do you express sin(π4)sin(7π8) without using products of trigonometric functions?

1 Answer
Apr 7, 2016

(2)(224)

Explanation:

P=sin(π4).sin(7π8)
Trig table --> sin (pi/8) = sqrt2/2
Trig unit circle -->
sin(7π8)=sin(π8)
Evaluate sin (pi/8) by using the thig identity:
cos2a=12sin2a
cos(π4)=22=12sin2(π8)
2sin2(π8)=122=222
sin2(π8)=224
sin(π8)=222 --> sin(π8) is positive.
Finally:
P=(2)(224)