document.write( "Question 1042538: Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1? \r
\n" ); document.write( "\n" ); document.write( "I need to show work \n" ); document.write( "

Algebra.Com's Answer #657507 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The amplitude is normally $\"+1+\"$ , so you
\n" ); document.write( "need a factor of $\"+2+\"$
\n" ); document.write( "The midline is normally $\"+0+\"$ , so you need
\n" ); document.write( "to add $\"+1+\"$ to the function
\n" ); document.write( "--------------------------
\n" ); document.write( "So far, it looks like
\n" ); document.write( " $\"+f%28x%29+=+2%2Acos%28+k%2Ax+%29+%2B+1+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "You ar told that:
\n" ); document.write( "when $\"+x+=+pi%2F3+\"$ then the cosine has gone
\n" ); document.write( "through an entire period, so it must be true:
\n" ); document.write( " $\"+k%2A%28+pi%2F3+%29+=+2%2Api+\"$
\n" ); document.write( " $\"+k+=+6+\"$
\n" ); document.write( "So, the function must be:
\n" ); document.write( " $\"+f%28x%29+=+2%2Acos%28+6x+%29+%2B+1+\"$
\n" ); document.write( "Here's a plot of 2 periods in both directions from
\n" ); document.write( " $\"+x+=+0+\"$ . It is plotted from $\"+x+=+-2%2Api%2F3+\"$ to
\n" ); document.write( " $\"+x+=+2%2Api%2F3+\"$
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\n" ); document.write( "( note that $\"+f%28pi%2F3%29+=+3+\"$ as it should ) \n" ); document.write( "

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