determine the quadrant adding or subtracting periods -10pi/3+2pi=-4pi/3+2pi=2pi/3 which is the second quadrant because first quadrant is between 0 and pi/2 second quadrant is between pi/2 and pi third quadrant is between pi and 3pi/2 fourth is between 3pi/2 and 2pi now we find the terminal angle since it is the second quadrant we use theta'=pi-theta=pi-2pi/3=pi/3 sin(pi/3)=sqrt(3)/2 sin is positive in the second quadrant cos(pi/3)=-0.5 cos is negative in the second quadrant tan(pi/3)=sin(pi/3)/cos(pi/3)=-sqrt(3) tan is negative in the second quadrant
