finding constants of a trigonometric function

[carlos08]

The desert temperature, H, oscillates daily between 44ºF at 5am and 84ºF at 5pm. Write a possible formula for H, measured in hours from 5am. Use the form H = Acos(Bt) + C

 

[Deleted member 4993]

The desert temperature, H, oscillates daily between 44ºF at 5am and 84ºF at 5pm. Write a possible formula for H, measured in hours from 5am. Use the form H = Acos(Bt) + C

From the given conditions:

H = 44 at t = 0 .. (5AM) → 44 = A + C

Also C = (44+84)/2

and H = 84 at t = 12 → 84 = Acos(12B) + C

Now continue......

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[stapel]

The desert temperature, H, oscillates daily between 44ºF at 5am and 84ºF at 5pm. Write a possible formula for H, measured in hours from 5am. Use the form H = Acos(Bt) + C

There's nothing here that requires calculus. Just use what you learned back in trig:

What is the minimum value? What is the maximum value? What is the difference between them? What then is the amplitude?

What is the value halfway between the max and min? What then is the "center line" of the graph (that is, what is the vertical shift)?

What is the length of time for one temperature cycle (all the way through, back to the beginning temperature)? What then is the length of the period?

If you get stuck, please reply showing your work and reasoning for each of these questions. Thank you!