We know that 2π/3 radians-------> convert to degrees-----> 2*180/3---> 120° 120°=90°+30°
Part a) Find <span>sin(2π/3) </span>sin(2π/3)=sin (90°+30°) we know that sin (A+B)=sin A*cos B+cos A*sin B so sin (90°+30°)=sin 90*cos 30+cos 90*sin 30 sin 90=1 cos 30=√3/2 cos 90=0 sin 30=1/2 sin (90°+30°)=1*√3/2+0*1/2-----> √3/2
the answer part a) is sin(2π/3)=√3/2
Part b) Find cos (2π/3) cos (2π/3)=cos (90°+30°) we know that cos (A+B)=cos A*cos B-sin A*sin B so cos (90°+30°)=cos 90*cos 30-sin 90*sin 30 sin 90=1 cos 30=√3/2 cos 90=0 sin 30=1/2 cos (90°+30°)=0*√3/2-1*1/2----> -1/2
