document.write( "Question 1108331: What is the equation of a cosine function with an amplitude of 4, a period of 3pi, a horizontal phase shift of pi/4 to the right, and a vertical shift down of 3 units? \n" ); document.write( "

Algebra.Com's Answer #723373 by greenestamps(13200) $\"\"$ $\"About$

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

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

\n" ); document.write( "In this form, |a| is the amplitude, c is the (horizontal) phase shift, and d is the vertical shift.

\n" ); document.write( "Note that in this form, the coefficient of x must be 1, in order for c to be the correct phase shift.

\n" ); document.write( "For b in the formula, you have to do a bit of work: b is $\"%282pi%29%2Fp\"$ where p is the period.

\n" ); document.write( "So in your example, a = 4, b = (2pi)/3pi) = 2/3, c = pi/4, and d = -3.

\n" ); document.write( " $\"4%2Acos%28%282%2F3%29%28x-pi%2F4%29%29-3\"$ \n" ); document.write( "

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