Question 969921
The amplitude is the absolute value of {{{a}}}: that is {{{abs(a)}}}, and  it is given that {{{a < 0}}}; so, if your amplitude is {{{4}}}, but {{{a}}} is less than zero, we have to use {{{-4}}} for {{{a}}}. 

{{{a=-4}}}

If our period is usually {{{2pi}}}, and in this case it is {{{(1/4)pi=pi/4}}}, everything has to go {{{8}}} times as fast, so {{{b= 8}}}.  

That will give us a function:

{{{y=-4*sin( 8* theta)}}}


{{{ graph( 600, 600, -10, 10, -10, 10,-4*sin( 8* x)) }}}