How Do You Determine the Period of a Graph with Unequal Maximums and Minimums?

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Determining the period of a graph with unequal maximums and minimums can be challenging without graphing software. The period of a periodic function is defined as the distance over which the function repeats itself. To find the period visually, one can analyze the distance between consecutive peaks or troughs on the graph. Repositioning the graph to align its center with the x-axis may help in visualizing the periodicity, but it's not strictly necessary. Understanding the definition of the period is crucial for accurately determining it from the graph.
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Homework Statement



So my book has a bunch of examples of graphs similar to sine or cosine graphs, where the maximums and minimums are the same (for example, the maximums might be 1, and the minimums will be -1). If I only have a graph to work with, I will just look at the waves and determine the period from that. But how do I determine the period of a graph that has unequal maximum and minimums? For example, all the maximums may be 7, but all the minimums will be 2. How do I determine the period of a graph like this, if I only have the graph to work with? Do I just move the graph so that its center is at the x axis? Is there anyway to determine the period of a graph like this without using graphing software to reposition the graph to the x axis? If I have to redraw it it could be difficult.

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priceofcarrot said:

Homework Statement



So my book has a bunch of examples of graphs similar to sine or cosine graphs, where the maximums and minimums are the same (for example, the maximums might be 1, and the minimums will be -1).

If I only have a graph to work with, I will just look at the waves and determine the period from that. But how do I determine the period of a graph that has unequal maximum and minimums? For example, all the maximums may be 7, but all the minimums will be 2. How do I determine the period of a graph like this, if I only have the graph to work with? Do I just move the graph so that its center is at the x axis? Is there anyway to determine the period of a graph like this without using graphing software to reposition the graph to the x axis? If I have to redraw it it could be difficult.
...

Thanks

What is the definition of the period of a periodic function?
 


Oh god that's embarrassing.. Lol

Sorry, I just checked my work today and can't believe that I asked this question.

Thanks
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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