Can anyone help explain and solve please??
The temperature of a chemical reaction ranges between 40°C and 180°C. The temperature is at its lowest point when t = 0 and completes one cycle over a 12-hour period. What is a sine function that would model this reaction?

Question

Can anyone help explain and solve please?? 
The temperature of a chemical reaction ranges between 40°C and 180°C. The temperature is at its lowest point when t = 0 and completes one cycle over a 12-hour period. What is a sine function that would model this reaction?

anonymous · Answer

f(x) = 70 sin 12x + 110 

 f(x) = 110 sin 12x + 70 

 f(x) = 70 sin pi over 6x + 110 

 f(x) = 110 sin pi over 6x + 70

anonymous · Answer

@dumbcow

anonymous · Answer

range if of length $180-40=140$ and therefor the number out front should be $70$  
ignore 2 and 5

anonymous · Answer

since the period is $12$ you can set $\frac{2\pi}{b}=12$ and solve for $b$

anonymous · Answer

you should get $b=\frac{\pi}{6}$

anonymous · Answer

What about the numbers being added? (in the beginning of each answer) what do they mean/how do I get those numbers? @satellite73

anonymous · Answer

@thomaster @robtobey @abb0t @iambatman @RadEn

dumbcow · Answer

$$y = A \sin (Bx + C) + k$$
min = k - A
max = k + A

period = 2pi/B

shift is determined by "C"
given point is that lowest point occurs at t=0  ..... (0, 40)
thus sin(Bx +C) = -1 when x=0
sin(C) = -1
C = -pi/2