ANSWER
[tex]y = 5\sin( \frac{\pi}{3} x - \frac{2\pi}{3} ) [/tex]
EXPLANATION
Let the equation of the sine curve be of the form;
[tex]y = a \sin(bx + c) [/tex]
where a=5 is the amplitude and period,
[tex] \frac{2\pi}{b} = 6[/tex]
This implies that
[tex]b = \frac{2\pi}{6} [/tex]
[tex]b = \frac{\pi}{3} [/tex]
We substitute the values we got so far into our equation to obtain;
[tex]y = 5\sin( \frac{\pi}{3} x + c) [/tex]
When we substitute (2,0) we obtain;
[tex]0= 5\sin( \frac{2\pi}{3} + c) [/tex]
Solve for c.
[tex] \sin( \frac{2\pi}{3} + c) = 0[/tex]
[tex]\frac{2\pi}{3} + c = \sin^{ - 1} (0)[/tex]
[tex]\frac{2\pi}{3} + c = 0[/tex]
[tex]c = - \frac{2\pi}{3} [/tex]
Hence our equation becomes
[tex]y = 5\sin( \frac{\pi}{3} x - \frac{2\pi}{3} ) [/tex]
The correct choice is D.
