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Question 1140827: Here is my question.
https://gyazo.com/3670cc816674121c9c5333f85ef18d99
And this is what I have so far. I just need help putting all this information into the equation. I don't understand that.
a is the amplitude;
the period is 360/b (assuming x is in degrees);
the horizontal shift is c (0 in this example);
d is the vertical shift (axis, or center line)
The center line is halfway between the minimum and maximum values; in this example the minimum and maximum values are 0 and 4. That gives you the value of d.
The amplitude a is half the difference between the minimum and maximum values.
because we are using a sine function the horizontal shift is 0.
The period is 180 degrees; that gives you the value of b.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i got it, but it wasn't easy.
i had to play around with the graph to understand what was going on.
the easier parts are as follows.
the highest value is 4 and the lowest value is 0.
that makes the amplitude 4 / 2 = 2.
that makes the vertical displacement equal to 2 because the center line has to be halfway between the high point and the low points.
the graph looks like it can be modeled with a cosine function, so that's what i used.
so far i have y = 2 * cosine (x) + 2.
the period is 180 degrees, so the frequency has to be 360 / 180 = 2.
that makes the equation y = 2 * cosine (2 * x) + 2.
the graph of that equation is shown below.
what's left is the horizontal shift.
at first i found it the easy way.
that was to create a horizontal line at y = 2.5 and then find that value of x on the graph gave me that.
it turned out that the value of y = 2.5 was at x = -37.761 degrees.
that graph is shown below.
to make that value of y = 2.5 show up when x = 0, i needed to shift the graph to the right 37.761 degrees.
the equation became y = 2 * cos(2 * (x - 37.761)) + 2.
that graph is shown below.
the graph now looks like what your diagram shoed you, even though that diagram was not that easy to figure out.
the hard way to figure out what to do for the horizontal displacement was as follows.
since the cosine function was displaced 2 unit vertically up, i figured that the value of the cosine function needed to be .5 when x = 0.
i used my calculator to find that the angle was 60 degrees because arc cosine (.5) = 60 degrees.
however, since the amplitude was 2, in order to get a cosine value of .5, i needed to get a cosine value of .25 because 2 * .25 = .5.
therefore i looked for the angle that had a cosine value of .25.
that angle was 75.52248781.
since it occured before x = 0, the angle was actually -75.52248781 degrees.
but, since the frequency was 2, i needed to get half of that angle which made it -37.76124391.
that's the angle i found by looking at the graph, only it was rounded to 3 decimal digits.
that was close enough for graphing purposes, so i got what i wanted without having to put in the full angle, i.e. the rounded angle to 3 decimal digits was good enough.
doing it from the graph as i initially did was much easier.
doing it from the equation and using some logic was much harder.
i did arrive at the same solution, however, which is good.
any questions, write to dtheophilis@gmail.com.
you were asked to determine the equation.
the equation is y = 2 * cosine (2 * (x - 37.76124391)) + 2
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