How do you express cos(π3)sin(11π8) without using products of trigonometric functions?

2 Answers
Apr 15, 2016

=12[sin(41π24)+sin(25π24)]

Explanation:

Use formula

sin(A+B)sin(AB)=2cosAsinB

cosAsinB=12[sin(A+B)sin(AB)]

A=π3andB=11π8

cos(π3)sin(11π8)=12[sin(π3+11π8)sin(π311π8)]

=12[sin(41π24)sin(25π24)]

=12[sin(41π24)+sin(25π24)]

Apr 16, 2016

(12)sin(3π8)

Explanation:

P=cos(π3).sin(11π8)
Trig table -->cos(π3)=12.
sin(11π8)=sin(3π8+π)=sin(3π8)
The product can be expressed as
P=(12)sin(3π8)

We can evaluate P by applying the identity: cos2a=12sin2a
cos(6π8)=cos(3π4)=22=12sin2(3π8)
2sin2(3π8)=1+22=2+22
sin2(3π4)=2+24
sin(3π8)=2+22 --> sin(3π8) is positive.
Finally,
P=(12).sin(3π8)=(14)2+2