Length of the Day Model
Great! I've copied your model from the previous activity below. I've also opened the "Algebra Perspective" of Geogebra. Notice this model involves the trigonometric function sine. Whenever you are modeling a process that oscillates, a sine function as a model is viable ("oscillate" means to returns back to where one started and then repeat). We'll discuss sine functions in their own right later.
As you've probably noticed by now, there's two ways you can explore any function/model in Geogebra:
- You can create points on the model by typing
(#,g(#))-- this is what you've done in most of the previous activities, or - You can just calculate only outputs by typing
g(#)-- we did this earlier.
g(25) into the input bar on the left next to the large "+" sign. This will create a number, a, which is between 568 and 569. This means that on the 25th day of the year, the model you created estimates that the length of the day is between 568 and 569 minutes.
Try out some other days. For instance, you can use this website to see what day of the year your birthday is, then put that number into g to see how many minutes the sun is above the horizon on your birthday. Can you find the longest day of the year? The shortest?
Later, we'll learn how to use Calculus to study the rate of change of this function to determine the longest and the shortest days of the year in Johnson, Vermont.
By the way, if you're wondering why the input bar looks different, it's because the "Algebra Perspective/Mode" must be open. Opening the Algebra Perspective moves the input bar to the left in Geogebra 6. If you download Geogebra 5 to your computer, the input bar doesn't move. All in all though, this is pretty unimportant.
Move forward to get started on the last few sections about functions.