Question 1091306
{{{y=sin(1/2(theta)-90 )-4 }}}

Use the form{{{ a*sin(bx-c)+d}}} to find the variables used to find the amplitude, period, phase shift, and vertical shift.

{{{a=1}}}
{{{b=1/2}}}
{{{c=90 }}}->{{{pi/2 }}}radians
{{{d=-4}}}

the amplitude is {{{a =1}}}
so, amplitude is:{{{ 1}}}


Find the period using the formula {{{2pi/b}}}=>{{{2pi/(1/2)=4pi}}}

period :{{{4 pi}}}

Find the phase shift using the formula {{{c/b}}}

{{{(pi/2)/(1/2)=2pi/2=pi}}}->

 the phase shift : {{{pi}}}

 the vertical shift is {{{d=-4}}}

Vertical Shift:  {{{4}}} units down

max{{{y = sin(theta/2 - 90) - 4 = -3 }}} at {{{theta = 180 + pi - 4 n *pi }}} for integer {{{n}}}

min{{{y = sin(theta/2 - 90) - 4 = -5}}} at {{{theta = 180 - pi - 4 n *pi}}}  for integer {{{n}}}

answer:

phase shift ____{{{pi}}}____ amplitude ___{{{1}}}_____ vertical displacement ___{{{4}}} units down___
max y–value ___{{{-3 }}}_____ min y–value ____{{{-5}}}________ period ___{{{4 pi}}}______