\( \definecolor{flatred}{RGB}{192, 57, 43} \definecolor{flatblue}{RGB}{41, 128, 185} \definecolor{flatgreen}{RGB}{39, 174, 96} \definecolor{flatpurple}{RGB}{142, 68, 173} \definecolor{flatlightblue}{RGB}{52, 152, 219} \definecolor{flatlightred}{RGB}{231, 76, 60} \definecolor{flatlightgreen}{RGB}{46, 204, 113} \definecolor{flatteal}{RGB}{22, 160, 133} \definecolor{flatpink}{RGB}{243, 104, 224}\)

February 22, 2021

Transforming Sinusoids - Exploration

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I noticed that a lot of people struggled with transforming sinusoids on the Desmos activity in class. I think part of this was that I left it so open-ended — it was difficult to really get a grasp of how all the different values of \(a\), \(b\), \(c\), and \(d\) affected the graphs of \(\color{flatblue}y=a\sin\big(b(x-c)\big)+d\) and \(\color{flatred}y=a\cos\big(b(x-c)\big)+d\).

So, in response, I've programmed a new Desmos activity that should make it easier to see how to transform the graphs as well as how to match a given sinusoidal curve.

Preview Activity 6

Answer these questions and submit your answers as a document on Moodle. (Please submit as .docx or .pdf if possible.)

On the Desmos activity above, turn the folders on for Curve 1, Curve 2, and Curve 3 by clicking the folder icons:

For each curve, find three different graphs that match it, including at least one sine and at least one cosine each. (So you should end up with nine equations total.)

  • Tip: Try letting \(a\) be negative sometimes to get more equations for the same curve.

Submit your nine equations, and then let me know if there was anything about this particular activity that made more sense than the one in class, or if there are still questions you have after doing it.

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