document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115522>Question 1115522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x) = cosx, write a function g(x) for the sinusoid that translates f(x) with the following transformations:\r<BR>\n" );
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document.write( "Reflected over the midline y=-3, with an amplitude of 3, twice the period, and a phase shift of pi/2 to the right. </SPAN>\n" );
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document.write( "The general cosine function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Acos%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"a%2Acos%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a is the amplitude;<BR>\n" );
document.write( "b determines the period (the period is 2pi/b);<BR>\n" );
document.write( "c is the horizontal phase shift; and<BR>\n" );
document.write( "d is the vertical shift.<br><BR>\n" );
document.write( "\"reflected...\"  --  that means a is negative<br><BR>\n" );
document.write( "\"...over the midline y=3...\"  --  that's a vertical shift; d is 3<br><BR>\n" );
document.write( "\"...with an amplitude of 3...\"  --  we already know a is negative; now this means a is -3<br><BR>\n" );
document.write( "\"...twice the period...\"  --  the period is 4pi; since the period is 2pi/b, b is 1/2<br><BR>\n" );
document.write( "\"...and a phase shift of pi/2 to the right  --  that means c is pi/2<br><BR>\n" );
document.write( "Put it all together, using the values of a, b, c, and d you have determined:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Acos%28%281%2F2%29%28x-pi%2F2%29%29%2B3 ALIGN=MIDDLE  ALT=\"-3%2Acos%28%281%2F2%29%28x-pi%2F2%29%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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