Find sine function from graph

In this math example, we are given the graph of a sinusoidal graph and tasked with finding the equation of the function that will produce the graph. We talk through the process of whether we should use the sine sin or cosine cos function. Then we walk through finding each piece of the function. First the amplitude is found by taking half of the difference between the highest y-value and the lowest y-value from the graph. Then we look at the period of the graph (distance left to right before it starts repeating). This is used to find a multiple for the inside of the function. We next note that the period of the function does not begin at the y-axis, this means that our graph has a horizontal shift. We apply this transformation by subtracting the appropriate value directly from x (inside the function). Finally, we observe a vertical shift. To find amount, we find the midline by calculating the average between the highest and lowest y-values on the graph. This value is added to the entire function to move the graph upwards. Once all of this information is gathered, we have the function that will produce the given graph.
This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al. It is an open-source textbook from OpenStax that you may download for
free at openstax.org/d.... The text is licensed under the Creative Commons Attribution license. creativecommon...