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

The find step is to find C which is the vertical shift. This is the average between the maximum and minimum. So its 30+70=100/2= 50. the amplitude (A) take the average of the difference between max. temp. and min. value 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