Question 1179525
{{{67}}} degrees at midnight
during the day are {{{76}}} and {{{58}}} degrees

find an equation for the temperature,

 {{{D(t)=a*sin(b(t-d))+c}}}

the average is:
{{{76-67=9}}}
{{{67-58=9}}}

amplitude ({{{a}}}) is {{{9}}};
period = {{{24}}} hours;

Assuming {{{t}}} is the number of hours since midnight when the temperature is falling amplitude {{{a}}} have negative sign
 

{{{a=-9}}}
{{{b=2pi/24=(1/12)pi}}}
{{{c=67}}}
{{{d=0}}}

{{{D(t)=-9sin((1/12)pi*t)+67}}}