document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143426>Question 1143426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of cos(T) is shifted left 270°, has the period decreased to 180°, and is shifted up 2 units. What is the transformed equation? </SPAN>\n" );
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document.write( "With the amplitude unchanged, the general equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28b%28T-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"cos%28b%28T-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where c is the horizontal (phase) shift and d is the vertical shift.  b is the normal period of 360 degrees, divided by the actual period.<br><BR>\n" );
document.write( "(1) The basic graph: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28T%29 ALIGN=MIDDLE  ALT=\"cos%28T%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Shifted 270 degrees left --> c = -270: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28T-%28-270%29%29+=+cos%28T%2B270%29 ALIGN=MIDDLE  ALT=\"cos%28T-%28-270%29%29+=+cos%28T%2B270%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) Period changed from 360 degrees to 180 degrees --> b = 360/180=2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282%28T%2B270%29%29 ALIGN=MIDDLE  ALT=\"cos%282%28T%2B270%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282T%2B540%29 ALIGN=MIDDLE  ALT=\"cos%282T%2B540%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(4) Shifted up 2 --> d = 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282%28T%2B270%29%29%2B2 ALIGN=MIDDLE  ALT=\"cos%282%28T%2B270%29%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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