The desert temperature oscillates daily between 4 degrees celsius at 5am and 32 degrees celsius at 5pm. Write a formula for the temperature as a function of time "t" measured in hours from 5am.

I know at t = 0, it is 5am.
Therefore, at t = 12, it is 5pm.
So, (0,4) is a minimum, and (5,32) is a maximum. Drawing just those points out, I can see that it is going to end up as a negative cosine function.

I figured that by taking the min and the max y-values and dividing by 2, I get the axis (or the vertical shift), which is 18. Now I am stuck.

I have (so far),
f(x) = -cos(x) + 18

Question

The desert temperature oscillates daily between 4 degrees celsius at 5am and 32 degrees celsius at 5pm. Write a formula for the temperature as a function of time "t" measured in hours from 5am.

I know at t = 0, it is 5am.
Therefore, at t = 12, it is 5pm.
So, (0,4) is a minimum, and (5,32) is a maximum. Drawing just those points out, I can see that it is going to end up as a negative cosine function.

I figured that by taking the min and the max y-values and dividing by 2, I get the axis (or the vertical shift), which is 18. Now I am stuck.

I have (so far),
f(x) = -cos(x) + 18

anonymous · Answer

I would like a hint as to what I should do next