Question

The desert temperature, H, oscillates daily between 30ºF at 4am and 70ºF at 4pm. Write a possible formula for H in terms of t, measured in hours from 4am. Use the form
H = A cos(Bt) + C.
A=
B=
C=

Answer 1

First find the C which is the vertical shift, which is max. plus min. divided by 2. So its 30+70=100/2= 50. Well to find the amplitude (A) take the max. temp. and subtract it to the min. value and divide that by 2. So 70-30= 40/2= 20, but it becomes -20 because the graph is shifted up 50 degrees and decreases to 30 at 4a.m.
Then the period is 2pi/B which is 2pi/24, which equals pi/12.
A=-20
B= pi/12
C=50

I hope I didn't confuse you.