document.write( "Question 1160905: For the following table of data, determine an equation of a cosine function that satisfies the given data.\r
\n" ); document.write( "\n" ); document.write( "The link to the table is here: https://gyazo.com/330133762196a7fabc67d017c4cc199a\r
\n" ); document.write( "\n" ); document.write( "I need steps also please \n" ); document.write( "

Algebra.Com's Answer #784320 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The general cosine function is

\n" ); document.write( " $\"y+=+a%2Acos%28b%28x-c%29%29%2Bd\"$

\n" ); document.write( "a is the amplitude
\n" ); document.write( "b is a constant that determines the period, or is determined by the period
\n" ); document.write( "c is the (horizontal) phase shift
\n" ); document.write( "d is the vertical shift (centerline of the graph)

\n" ); document.write( "The given data is the following:


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document.write( "x (degrees) -60 -30  0  30  60  90 120
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document.write( "y            10   8  6   8  10   8   6

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document.write( "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.

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document.write( "It also tells us that the period is 120 degrees; that means parameter b is 360/120 = 3.

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document.write( "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.

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document.write( "Now we have all the parameters we need to write the equation:
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document.write( "a = 2
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document.write( "b = 3
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document.write( "c = 60
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document.write( "d = 8

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document.write( "Here is a graph, showing constant functions at the minimum and maximum values and the center line....

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