Question 1160905
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The general cosine function is<br>
{{{y = a*cos(b(x-c))+d}}}<br>
a is the amplitude
b is a constant that determines the period, or is determined by the period
c is the (horizontal) phase shift
d is the vertical shift (centerline of the graph)<br>
The given data is the following:<pre>
x (degrees) -60 -30  0  30  60  90 120
y            10   8  6   8  10   8   6<br>
The function completes a cycle between (-60,10) and (60,10); 10 is the maximum value; 6 is the minimum value; 8 is the centerline value.  That immediately tells us d=8 and a=2.<br>
It also tells us that the period is 120 degrees; that means parameter b is 360/120 = 3.<br>
Finally, the basic cosine function has its maximum value at x=0.  The given function has a maximum values at x=60; so c is 60.<br>
Now we have all the parameters we need to write the equation:
a = 2
b = 3
c = 60
d = 8<br>
{{{y = 2cos(3(x-60))+8}}}<br>
Here is a graph, showing constant functions at the minimum and maximum values and the center line....<br>
{{{graph(540,400,-60,120,-2,12,y = 2cos(3(pi/180)(x-60))+8,6,8,10)}}}