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You can put this solution on YOUR website!
your equation is:
\n" ); document.write( " f(x) = 4cos(3x)+1
\n" ); document.write( "you want to shift it to the right by pi/12.
\n" ); document.write( "this means that if x is equal to pi/12, you want to get the cosine of x = 0.
\n" ); document.write( "the result of that is that the cosine of 0 is now the cosine of pi/12 which means that value has been shifted to the right by pi/12.
\n" ); document.write( "the general formula for a trigonometric function is:
\n" ); document.write( "y = a*cos(b(x-c))+d
\n" ); document.write( "a is the amplitude.
\n" ); document.write( "b is the frequency
\n" ); document.write( "c is the horizontal shift
\n" ); document.write( "d is the vertical shift of the center line.
\n" ); document.write( "your equation has an amplitude of 4 and a vertical shift of 0.
\n" ); document.write( "your equation has a frequency of 3 which means the period is equal to 2*pi/3 which makes it equal to (2/3)*pi instead of the 2*pi that it normally is.
\n" ); document.write( "based on what you have, the standard form of your equation would be:
\n" ); document.write( "f(x) = 4*cos(3*(x-0))+1
\n" ); document.write( "a graph of your equation looks like this:
\n" ); document.write( "
\n" ); document.write( "a vertical line is shown at x = pi/12 to show you where your shift will occur.
\n" ); document.write( "since you want to shift the graph to the right, then the value of cosine at x = 0 will then become the value of cosine at x = pi/12.
\n" ); document.write( "to do this, your equation has to go from:
\n" ); document.write( "f(x) = 4*cos(3*(x-0))+1
\n" ); document.write( "to:
\n" ); document.write( "f(x) = 4*cos(3*(x-(pi/12)))+1
\n" ); document.write( "the graph of that equation looks like this:
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "