ANSWER
[tex]y = 5 \sin( \frac{6}{5} x - \pi)-4 [/tex]
EXPLANATION
The given function is
[tex]y = 5 \cos( \frac{3}{5} x - \pi) + 4[/tex]
The period of this function can be determined using the formula:
[tex]T= \frac{2\pi}{ |b| } [/tex]
.
The period is
[tex]T= \frac{2\pi}{ \frac{3}{5} } = \frac{10\pi}{3} [/tex]
Half the period of this function is:
[tex] \frac{ \frac{10\pi}{3} }{2} = \frac{5\pi}{3} [/tex]
The function which has this period is
[tex]y = 5 \sin( \frac{6}{5} x - \pi) -4[/tex]
The first choice is correct.
