We would like to find the exact value of sin((3pi)/4), First, we can find the reference angle of (3pi)/4 where pi-sin((3pi)/4)=pi/4, so the reference angle is pi/4. Now the next step is to define the sign of (3pi)/4. We know that (3pi)/4 is in quadrant 2 which the sine function is positive in this quadrant, so the value of sin(3pi)/4 is positive and we can simplify it as follows: sin(3pi)/4=sin(pi-pi/4)=sin pi/4 Note that the first step was to find the reference angle and then was to define the sign of sin(3pi)/4. Now we can find the value of sin(3pi)/4 by knowing the value of sin pi/4 which equals sqrt2/2 sin (3pi)/4=sin(pi-pi/4)=sin pi/4=sqrt2/2