Hello, I need help with a project. I have the data provided but I just need help turning it into a trig function. Thank you! You don't have to answer the Predictions Portion, I just wanted to add them to provide additional insight as to what the project. If the data I have is not applicable please let me know. Thank you! :)

No need to answer the prediction questions unless you would like to:

Predictions Spoiler alert, in this project you will be modelling your very own trigonometric function after something you observe in your daily life. So how do you think you'd go about that? If you were tasked with collecting data that could follow a trigonometric function, describe your procedure here: Once we have our data, describe how you think you'd take your observations and transform them into a trigonometric function here:What problems do you predict running into when modelling your data into a trigonometric function? Do you think your data will fit perfectly into an equation? Why or why not? In the next section we will look at what collecting data will look like and the real procedure for creating the trigonometric function that it models.Experiment In this section of the project, we will be collecting data from observations in order to make our very own trigonometric function. But before we do that, let's quickly go over what a trigonometric function is and does so that we understand what we are trying to observe. Trigonometric functions, such as the sine function or cosine function create repetitive, wave-like graphs that bounce back and forth between a maximum and minimum value. This works well when we are dealing with something that happens repetitively over a certain period of time, in which case for y = f(), we have that the "x" variable is the time and the "y" variable is the value of what we are observing. So in order to make our function model as accurately as we can there are a few guidelines we should follow. 1.) Since trigonometric functions oscillate (or fluctuate) between two values, these values should be the same over each period of the function. That is the maximum value should always remain quite constant, as should the minimum value. For example, I could observe the high and low temperatures during a relatively stable season, where the daily highs are always very similar, and the lows are also very similar. 2.) The time between observations should be relatively equal. This time is known as the period of the function, and if it changes from observation to observation we end up with a lopsided graph which is more difficult to accurately model. In the example of the temperature observations in 1), the daily highs and daily lows usually happen at the same time of the day, so the period of the function is relatively constant. 3) You should be observing the highest and lowest values that your variable can take. It's much more difficult to model something if you're only taking an average value over the duration of the observations. This makes it pretty impossible to find those maximum and minimum values we need in order to form a proper trigonometric function. So now that we know our guidelines for how and what we should be observing for the experiment, we can begin thinking about the possible things to collect data on. Some examples are daily high and low temperatures, the percentage of the visible moon over the 27 day moon cycle, electricity usage of your household during certain times of the day. Use information from the internet if you wish, in real time or data that been collected in the past. Describe what you are observing here (give a description of the time between observations as well):Your "Max Value" should be the largest value you would observe, and your "Min Value" should be the smallest value. The time can be the amount of time that passes from one observation to the next, in which case the first value would be 0. Or the time can just be the time of day when you make the observation.Model Now that we have our data, we can begin to model it into a trigonometric function. We find our amplitude, period, and vertical displacement from our observations. Do we use a sine or cosine function? Well, that's up to you. What would be easier if you used your "Max Value" at time 0? Just some things to think about when making your equation. Amplitude: Period: Vertical Displacement: Your equation should be in the form: f(x) = asin(bx) + c f(x) = acos(bx) + c Equation: That's it! You've done it. You've successfully modelled what you saw in real life into a trigonometric function. Pretty cool.REFLECTION Did you choose to model your data using a sine or a cosine function? Why? Use your new found function to find certain maximum or minimum values at the times you observed while collecting your data. Do these values exactly match your observations? If not, describe why your function is not 100% accurate.If you were to use the first maximum observed value at time, t = 0 (which you may have done), how does that simplify the trigonometric function? If you were to do this project over again, what would you do differently, and why?So now that we know what you will be observing, you can list your data here: Observations Value Time Max Value 1 38.4 'c 12 p.m. Min Value 1 12'c 12 a.m. Max Value 2 32'c 12 p.m. Min Value 2 9.6'c 12 a.m. Max Value 3 48.2 c 12 p.m. Min Value 3 17.8'c 12 a.m. Max Value 4 39'c 12 p.m. Min Value 4 14.3'c 12 a.m