y=-cos(8x)
This is how I would go about understanding and building this equation.
I would always do a rough graph whether I was asked to or not.
y=cosx looks like this you must memorize this
But mine has a cos(8x)......
y=cos(8x)
but my wavelength is 2pi/8 so the middle must be pi/8
mmm so now I have so the 2pi on the x axis must be replaced with 2pi/8, and the middle will be half that, pi/8
I sketch that.
then it is multiplied by -1 so I turn it upside down.
Here I have built it.
The black one is the finished one
Mmm, it would be so much easier if you were in front of me. It would be much easier to explain.
Maybe I might half give up on that approach.
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Graph this. Do not use desmos except at the very end to check
y=3sin4x - 2
midline=? draw it with a dotted line.
what is the y value for the highest point, put a light line across to indicate the top.
what is the y value for the lowest point, put a light line across to indicate the bottom.
Will the y intercept be in the middle or at the top or bottom? put it in.
What is the wavelength?
Divide the wavelength by 4 and put the 4 points on the x axis. (so you will have 1 whole wavelength.)
Now graph it, or at least try to. See how you go.