Austin - in your question, you indicate that the domain for x is [-10,10], yet you have
which (when corrected for 2*pi) only returns am array of two elements
of the domain for [-10/pi, 10/pi]. Instead, use linspace to generate a linearly spaced vector/array of elements for your domain. For example,
x = linspace(-10,10,2000);
will generate 2000 elements that are linearly spaced in the interval [-10,10].
Now you want to only plot those values of y that are real, and ignore those that are complex (with non-zero imaginary components). The latter occur whenever sin(x) is negative. You can ignore these by setting them to NaN as
y = sin(x);
y(y<0) = NaN;
and plot the square root as
Try the above and see what happens!