How do you express sin(π8)cos((2π3) without using products of trigonometric functions?

1 Answer
Oct 31, 2016

222

Explanation:

P=sin(π8).cos(2π3)
Trig table --> cos(2π3)=12, then P can be expressed as:
P=(12)sin(π8)
We can evaluate the value of sin (pi)/8 by the trig identity:
2sin2(π8)=1cos(2π8)=1cos(π4)=122
sin2(π8)=224
sin(π8)=222
Only the positive value is accepted because sin(π8) is positive
Finally,
P=(12)sin(π8)=224