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# sinusoidal function equations 1

This short problem solution video explains how to find the equation of a sinusoidal function. The "Bias" or axis is given as y=5 and the coordinates of two sequential minimums are given.

Rather than trying to match numbers to letters in a standard equation form I attempt to solve this by relating it to translations and stretching in the plane. I also explain that there are multiple solutions (infinite actually). The x shift (or phase) can be + or 1, any multiple of the wavelength can be added to the phase, and a cosine can be used rather than a sine.

Minor errata: At 7:35I write the final equation on paper and I left the -5 on the left off intending to add +5 on the right but did not do so. Everything in Desmos is correct but the y= equation on paper needs a +5 on the right side.

Also at 10:20there is a bit of confusion when putting the phase into the cosine version. This arose because the slider for phi was not reset to zero and still had a value from the sin equation in it.

A link to the Desmos page I used will be added to the listing on my academic and tutoring website: https://jamesfrankenfield.comunder Academic/Tutoring Library - Videos; if you have problems finding that or questions about the video you can post a comment here or use the Contact page on my website.

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 By James Frankenfield Added May 26

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