Use the Sine to Show the Number of Daylight Hours in a Location
The graphs of sine curves and the cofunction, cosine, are useful for modeling situations that happen over and over again in a predictable fashion. Some examples include the weather, seasonal sales of goods, body temperature, the tide’s height in a harbor, average temperatures, and so on.
Here’s an example: San Diego, California, is a gorgeous part of the world. Whether it’s summer or winter, you want to be there. But what if you’re someone who likes long, sunny days? When is the best time to go there?
Assume that the following formula gives you the number of hours of daylight in San Diego when you input any day of the year. Letting t be the day of the year (from 1 to 365), you can figure the number of hours of sunlight, H, if you enter a value for t in the equation H(t) = 2.4 sin (0.017t – 1.377) + 12. The following figure shows the graph of this equation.