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.