How do you express cos( (15 pi)/ 8 ) * cos (( 4 pi) /3 ) cos(15π8)cos(4π3) without using products of trigonometric functions?

1 Answer
Sep 18, 2016

-(1/2)cos (pi/8)

Explanation:

Use trig table of special arcs and unit circle -->
cos ((15pi)/8) = cos ((16pi)/8 - pi/8) = cos (2pi - pi/8) = cos - pi/8 = cos (pi/8)cos(15π8)=cos(16π8π8)=cos(2ππ8)=cosπ8=cos(π8)
cos ((4pi)/3) = cos (pi/3 + pi) = - cos (pi/3) = - 1/2cos(4π3)=cos(π3+π)=cos(π3)=12
cos ((15pi)/8) = cos (-pi/8 + 2pi) = cos (-pi/8) = cos (pi/8) cos(15π8)=cos(π8+2π)=cos(π8)=cos(π8)
The product can be expressed as:
P = -(1/2)cos (pi/8)