document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163197>Question 1163197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> translate the graph of y=cos(x) to the left by pi/2 units, and then reflect this curve about the x-axis. what graphs results? </SPAN>\n" );
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document.write( "Graphically....<br><BR>\n" );
document.write( "(1) y = cos(x)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C-2pi%2C2pi%2C-2%2C2%2Ccos%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C-2pi%2C2pi%2C-2%2C2%2Ccos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Translate pi/2 to the left means cos(x) becomes cos(x+pi/2)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C-2pi%2C2pi%2C-2%2C2%2Ccos%28x%2Bpi%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C-2pi%2C2pi%2C-2%2C2%2Ccos%28x%2Bpi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) Reflect over x axis means cos(x+pi/2) becomes -cos(x+pi/2)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C-2pi%2C2pi%2C-2%2C2%2C-cos%28x%2Bpi%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C-2pi%2C2pi%2C-2%2C2%2C-cos%28x%2Bpi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The resulting graph is the graph of sin(x).<br><BR>\n" );
document.write( "Algebraically....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-cos%28x%2Bpi%2F2%29+=+-%28cos%28x%29cos%28pi%2F2%29-sin%28x%29sin%28pi%2F2%29%29+=+-%28cos%28x%29%280%29-sin%28x%29%281%29%29+=+sin%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );