The maximum value of the function y= -3+4 cos(5pi/6(x+4)) can be determined by differentiating the equation then make the derived function equal to zero. In this case, the function becomes 4 sin (5pi/6(x+4)) * (5pi/6) or equal to 10pi/3 sin (5pi/6(x+4)) = 0. sin -1 of 0 is equal to zero. hence, 5pi/6(x+4) should be zero. x is equal to -4. substituting -4 in the original equation,y= -3+4 cos(5pi/6(-4+4)) is equal to 1. The maximum value is 1.