Question 947646
A sinusoid is the name given to any curve that can be written in the form

{{{y=Asin(B(x-C))+D}}}  ................({{{A}}} and {{{B}}} are positive). 


|{{{A}}}| = {{{amplitude}}}

{{{B}}} = cycles from {{{0}}} to {{{2pi}}}

{{{period =2pi/B}}}

{{{D }}}= vertical shift (or displacement)

{{{C }}}= horizontal shift (sometimes called "phase shift" when {{{B = 1}}})


you have

{{{y = 5 sin (3(x-2))- 1 }}}

so,
 
|{{{A}}}| = {{{5}}}  (amplitude)

{{{B =3 }}}     (cycles from {{{0}}} to {{{2pi}}})

{{{period =2pi/B=2pi/3}}}

{{{D =-1}}} vertical shift (or displacement {{{1}}} unit {{{down}}}) 

{{{C =2}}}  ( horizontal shift, {{{2}}} units {{{left}}})


max{{{y = 5 sin(3 (x-2))-1}}}} = {{{4}}} at {{{x = 2+pi/6+(2n*pi)/3}}}  for integer {{{n}}}

min{ {{{y = 5 sin(3 (x-2))-1}}}} ={{{ -6}}} at {{{x = 2+pi/2+(2n*pi)/3}}}  for integer {{{n}}}