Cannot seem to figure out this inverse trig function problem

[colejr]

Question:
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 83 degrees and the low temperature of 67 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

D(t)=

---------
So far I've come up with this -16sin(pi/12)
This could be completely wrong as far as I know.

 

[Deleted member 4993]

Question:
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 83 degrees and the low temperature of 67 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

D(t)=

---------
So far I've come up with this -16sin(pi/12)
This could be completely wrong as far as I know.

You say: So far I've come up with this -16sin(pi/12)

What is that - what does that represent?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Cubist]

I guess that you obtained the 16 by subtracting the high temperature from the low (83-67). That's a good guess, however 16sin(?) would produce a temperature variation of 32 degrees, from -16 to +16. Can you try to correct this? For the final answer you're aiming for something that looks like this:-

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

but you need to find the values for a,b,c and d. Let's start by obtaining a and b, then we can think about c and d