Question 1206911
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A minimum value of a sinusoidal function is at (𝜋/4, 3). The nearest maximum value to the
right of this point is at (7𝜋/12, 7). Determine an equation of this function. Please how all your wonderous work.
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<pre>
This sinusoidal function is between 3 and 7 on vertical axis, so the midline is
y= {{{(3+7)/2}}} = 5  and the amplitude is 2 units.


The smallest distance between the minimum and the maximum is  

    {{{7pi/12}}} - {{{pi/4}}} = {{{7pi/12}}} - {{{3pi/12}}} = {{{(7pi-3pi)/12}}} = {{{4pi/12}}} = {{{pi/3}}}.


along the horizontal axis. Hence, the period T is twice this value, i.e.  T = {{{2pi/3}}}.


Having the minimum at ((𝜋/4, 3), we can use negative cosine with the argument centered at 𝜋/4

    y = {{{-2*cos(2pi*((x-pi/4)/T))+7}}} =  {{{-2*cos(3x-3pi/4)+7}}}.
</pre>

Solved.


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Post-solution note


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    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The rules of this forum (and the common sense) do not recommend make it.


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    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;No one forum for Math help does allow packing more than one problem per post
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