What are the x coordinates of the local maximum and local minimum of sin(x in the interval [0, 2π?

I am assuming you meant y=sin(x) from 0 to 2pi? Remember that the maximum and minimum points on the sine graph will occur 1/4 and 3/4 through the cycle, or period and the zeros occur at the beginning, middle and end. So you want to find the distance 1/4 of the way to 2pi and 3/4 of the way to 2pi. 
With this information, you can easily calculate your )

88 and -88. are absolute values and opposite integers