# Thread: Possible formula for oscillating temperature.

1. ## Possible formula for oscillating temperature.

The desert temperature, H, oscillates sinusoidally between 40°F at 5 am and 80°F at 5 pm. Write apossible formula for H in terms of t, measured in hours since midnight.

I graphed a sinusoidal function and determined that the midpoint = 60 degrees F, the period = (2pi)/B = 12 , so B = pi/6, and amplitude = -20. No phase shift, no vertical shift.

I used Asin(Bx + C) +D to get H(t) = -20sin(pi/6)x + 60 as my answer.

I normally like to try these problems to see if I can figure them out but I always appreciate when someone looks over my work and lets me know if I made a mistake and helps guide me in the right direction. Thanks in advance to anyone who looks at this.

2. ## Re: Possible formula for oscillating temperature.

Try to get into the habit of checking your answers. For this example, substituting t(x?) = 5 and t = 17 should get you temperatures of 40 and 80 respectively.

It doesn't work does it ?

Think again about the period, (it isn't 12), and also the phase shift, (it isn't zero).
Ask yourself at what times you want your first term to be zero, giving you a temperature of 60.