A smooth periodic curve passes through the origin O(0,0). Moving in the positive x-direction, the curve attains its first maximum value 1 at x=2π and its next minimum value −1 at x=23π. Thereafter the pattern repeats indefinitely in both directions.
a. (i) Prove that the curve satisfies the equation y=sinx for all real x.
b. (ii) Write a general expression for all x-coordinates at which the curve attains its maxima and another for all x-coordinates at which it attains its minima.
c. (iii) Determine the complete set of zeros of the curve.