Question 1117209
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We are looking (I assume) for equations of the position as<br>
{{{a*sin(b(x-c))+d}}}<br>
and<br>
{{{a*cos(b(x-c))+d}}}<br>
(1) The minimum and maximum values are 5 and 17. That means a is 6 and d is 11.<br>
(2) The minimum and maximum occur 24 seconds apart; that means the period is 48 seconds.  Then b is {{{(2pi)/48}}} = {{{pi/24}}}.<br>
(3a) For the sine function, the "start" of the period is when the value is 0 and increasing; that occurs at 18 seconds, so c is 18.<br>
(3b) For the cosine function, the "start" of the period is when the value is maximum; that occurs at 30 seconds, so c is 30.<br>
The two functions are<br>
{{{6*sin((pi/24)(x-18))+11}}}<br>
and<br>
{{{6*cos((pi/24)(x-30))+11}}}<br>
Here are graphs of the two functions; the sine graph (red) is shifted up 1 unit and the cosine (green) graph down 1 unit so you can see the graphs of both functions.<br>
{{{graph(400,400,-6,60,-4,20,6*sin((pi/24)(x-18))+12,6*cos((pi/24)(x-30))+10)}}}