How do you express cos(π3)sin(9π8) without using products of trigonometric functions?

1 Answer
Jun 24, 2016

P=(12)sin(π8)

Explanation:

Product P=cos(π3).sin(9π8)
Trig table --> cos(π3)=12
sin(9π8)=sin(π8+π)=sin(π8)
P can be expressed as:
P=(12)sin(π8).
Note. We can evaluate sin(π8) by using the trig identity:
cos2a=12sin2a.
cos(2π8)=cos(π4)=22=12sin2(π8)
sin2(π8)=12=224
sin(π8)=222.
Take the positive value since sin (pi/8) is positive.
P=(14)22