Determine all real numbers x that satisfy the inequality sin(2x+4π)>cos(3x−6π).
(i) Rewrite the inequality so that it involves only one basic trigonometric ratio of a single angle.
(ii) Find the complete set of solutions in the interval 0≤x<2π.
(iii) Extend the result of part (ii) to obtain the general solution for all real x.
(iv) Sketch, on the same set of axes, one complete period of each of the two trigonometric functions involved, and shade the portions of the x–axis corresponding to the solution set found.