document.write( "Question 1182157: State the amplitude, period, phase shift, and equation of midline/axis of curve, x and y axis for f(x) = 3cos(1/2x+90) −1 \n" ); document.write( "

Algebra.Com's Answer #812144 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"f%28x%29+=+3cos%28%281%2F2%29x%2B90%29%29-1\"$

\n" ); document.write( "Rewrite the function so the coefficient on x is 1:

\n" ); document.write( " $\"f%28x%29+=+3cos%28%281%2F2%29%28x%2B180%29%29-1\"$

\n" ); document.write( "That is in the form

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

\n" ); document.write( "In that form...

\n" ); document.write( "a is the amplitude
\n" ); document.write( "b determines the period (the period (in degrees) is 360/b)
\n" ); document.write( "c is the horizontal shift (phase shift)
\n" ); document.write( "d is the vertical shift (determines the midline)

\n" ); document.write( "So in this function...

\n" ); document.write( "a is 3
\n" ); document.write( "b is 1/2; the period is 360/b = 360/(1/2) = 720 degrees
\n" ); document.write( "c is -180 degrees
\n" ); document.write( "d is -1

\n" ); document.write( "ANSWERS:
\n" ); document.write( "amplitude 3
\n" ); document.write( "period 720 degrees
\n" ); document.write( "phase shift -180 degrees
\n" ); document.write( "midline y=-1

\n" ); document.write( " \n" ); document.write( "

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