How do you express cos( (5 pi)/4 ) * cos (( 2 pi) /3 ) cos(5π4)cos(2π3) without using products of trigonometric functions?

1 Answer
Mar 25, 2016

sqrt2/424

Explanation:

P = cos ((5pi)/4) .cos ((2pi)/3)P=cos(5π4).cos(2π3)
Trig unit circle and trig table give -->
cos ((5pi)/4) = cos (pi/4 + pi) = -cos (pi/4) = -sqrt2/2cos(5π4)=cos(π4+π)=cos(π4)=22
cos ((2pi)/3) = cos (-pi/3 + pi) = - cos pi/3 = - 1/2cos(2π3)=cos(π3+π)=cosπ3=12
P = (-sqrt2/2)(-1/2) = sqrt2/4P=(22)(12)=24