Kyle M. answered • 04/13/19

Learn all the "trig tricks" you'll need with a process that works

If we suppose a standard 24 hour day, and that there would only be one high point of temperature during a day, this implies that our period is length 24. Taking the difference of the maximum temperature with the average temperature gives us the amplitude. The average temperature is the vertical shift of the graph. There is no horizontal shift needed if we use the **sin **function, since the function reaches a critical value every 6 hours (either a maximum, minimum, or average). Since the temperature start off going down (instead of up like the **sin** parent function) we need to have a negative out front. Therefore, the resulting function would be y=-16**sin**((π/12)x)+65 and you could use that to find the temperature at any hour (hours after noon would be in military time). Thus, for 11AM (or 1100 hours) you would simply plug in 11 for x and get out approximately 61^{o}