Sinusoidal Function Context and Data Modeling Practice Test

Daylight duration in Anchorage, Alaska, changes dramatically across seasons and can be modeled sinusoidally. Approximate daylight (hours) on the 21st: Jan 5.8, Feb 8.6, Mar 12.0, Apr 15.6, May 18.6, Jun 19.4, Jul 18.2, Aug 15.2, Sep 12.5, Oct 9.2, Nov 6.5, Dec 5.5. The maximum is 19.4 and minimum is 5.5, so amplitude is 6.95 and vertical shift is 12.45. The period is 12 months, and the phase shift should place the peak near June. Using the information given in the scenario, what period should be used to fit the data accurately?

Average monthly temperatures in Denver, Colorado, follow a yearly cycle. Suppose average daily mean temperatures (°F) are: Jan 30, Feb 32, Mar 40, Apr 48, May 58, Jun 68, Jul 74, Aug 72, Sep 63, Oct 51, Nov 39, Dec 31. The maximum is 74 and the minimum is 30, so amplitude is 22 and vertical shift is 52. The period is 12 months, and the phase shift should place the peak near July. Based on the data presented, which sinusoidal function best models temperature $T(m)$, where $m$ is months after January (so $m=0$ is January)?