The phase shift term should be positive: the standard form is y = Asin(b(x-c))+kMy answer: y=9.67sin(t/6.17pi - 2.68pi/6.17) + 12.25
Also, the question is asking for a cosine function.
Apart from that, looks good.
Excellent2. The mean average temperature for Fairbanks, Alaska is 27 degrees F. The monthly average temperatures vary between 36.5 degrees above and below this value. If t=0 represents February, the phase shift of the sine function is 2.
a. Write a model for the average monthly temperature in Fairbanks.
My answer: y=36.5sin(t/6pi-pi/3)+27
b. According to your model what is the average temperature in November?
My answer: y(9) = 8.8 degrees
You need to add 5 for the "relative to lowest point bit" as that part tells you that the lowest point is considered 0 and hence the average will be 5. The negative sign out the front shouldn't be there.3. Stan observes a raft floating on the water bobbing up and down through a total amplitude of 5 feet. Beginning at the top of the wave, if the raft completes a full cycle every 5 seconds, what is the height of the raft relative to its lowest point after 32 seconds?
My answer: -5cos[2pi/5(32)]=4.04 ft.