# Thread: Setting up an equation...

1. ## Setting up an equation...

The desert temperature, H, oscillates daily between 36ºF at 6am and 76ºF at 6pm. Write a possible formula for H in terms of t, measured in hours from 6am. Use the form
H = A cos(Bt) + C.

Ok, so I'm setting this up like this...
A = 20 (I subtracted 36 from 76 and divided it in half)
B = 1pi/6 (the number of hours, 12 hours between 6am and 6pm and then reduced it)
C = 36

I know these values are wrong, but i cant set this up correctly can anyone help me out?

2. Originally Posted by JAMESveeder
The desert temperature, H, oscillates daily between 36ºF at 6am and 76ºF at 6pm. Write a possible formula for H in terms of t, measured in hours from 6am. Use the form
H = A cos(Bt) + C.

Ok, so I'm setting this up like this...
A = 20 (I subtracted 36 from 76 and divided it in half)
B = 1pi/6 (the number of hours, 12 hours between 6am and 6pm and then reduced it)
C = 36

I know these values are wrong, but i cant set this up correctly can anyone help me out?
The value of A is ok as far as its size, but note that the curve starts at a low point, rises to a high point at mid-cycle, then returns to the low point. that would be a "flipped" cosine curve, wouldn't it?
so ... what would you do to the value of A to show that?

the period is 24 hours ... 6AM to 6PM is half a cycle.

$B = \frac{2\pi}{24} = \frac{\pi}{12}$

$C = \frac{36+76}{2} = 56$