Scientists Sometimes Use the Formula $f ( t ) = a \sin ( b t + c ) + d$

Scientists sometimes use the formula $f ( t ) = a \sin ( b t + c ) + d$ to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in ${ } ^ { \circ } \mathrm { C }$ , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature is 19 ${ } ^ { \circ } \mathrm { C }$ , and the low temperature of -19 ${ } ^ { \circ } \mathrm { C }$ occurs at 4 A.M.

A) $a = 19 , b = \frac { \pi } { 24 } , c = - \frac { 5 \pi } { 6 } , d = 0$
B) $a = 25 , b = \frac { \pi } { 12 } , c = - \frac { \pi } { 6 } , d = 25$
C) $$a = 38 , b = \frac { \pi } { 6 } , c = - \frac { 5 \pi } { 6 } , d = 0$$
D) $a = 19 , b = \frac { \pi } { 24 } , c = - \frac { \pi } { 3 } , d = - 25$
E) $a = 19 , b = \frac { \pi } { 12 } , c = - \frac { 5 \pi } { 6 } , d = 0$

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