Precalculus, Chapter 4, 4.4, Section 4.4, Problem 62

sin(7pi/6)=sin(pi+pi/6)=-sin(pi/6)=-1/2
cos(7pi/6)=cos(pi+pi/6)=-cos(pi/6)=-sqrt(3)/2
tan(7pi/6)=tan(pi+pi/6)=tan(pi/6)=1/sqrt3