isn't this Q from the destroyer?? I remember it.. anyways look for the reference angle.. 116 degrees passes the 90 degree mark right? so.. 180-116= 64 degrees. so cos 116 is equal to cos 64. however, you must use CAST like you said. this means starting from quadrant 4, write CAST counterclockwise. C=cos is positive here, A means all in Q1 are +, S means all in Q2 are +, T means all in Q3 are +. so ur cos 64 actually becomes -cos64.
therefore, cos 116= -cos64