document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189886>Question 1189886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm really stuck on these two questions from trigonometry. Any chance I could get some help? Thanks in advance!\r<BR>\n" );
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document.write( "https://drive.google.com/file/d/11VL_RMNxbHDdBnerDPi9ifWkRZIJDfMD/view?usp=sharing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821392 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general transformations for the sine function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sin%28theta%29 ALIGN=MIDDLE  ALT=\"y+=+sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Asin%28b%28theta+-c%29%29+%2B+d ALIGN=MIDDLE  ALT=\"y+=+a%2Asin%28b%28theta+-c%29%29+%2B+d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+ ALIGN=MIDDLE  ALT=\"a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> vertical dilation (stretch) of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=amplitude ALIGN=MIDDLE  ALT=\"amplitude\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > => horizontal compression (shrink) of the period- defined as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Fb ALIGN=MIDDLE  ALT=\"2pi%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > => horizontal shift (left/right) The phase shift is defined as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fb ALIGN=MIDDLE  ALT=\"c%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+ ALIGN=MIDDLE  ALT=\"d+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> vertical shift (up/down)\r<BR>\n" );
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document.write( "Equation........Amplitude........Period........HorizontalTranslation........Equation of Midline\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%28x-3%29%2B1 ALIGN=MIDDLE  ALT=\"y=sin%28x-3%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Amplitude......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Period.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F1+=2pi ALIGN=MIDDLE  ALT=\"2pi%2F1+=2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Horizontal Translation.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units right)<BR>\n" );
document.write( "Equation of Midline.............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6sin+%280.25%28x%2B+45+%29%29-+9 ALIGN=MIDDLE  ALT=\"y+=+6sin+%280.25%28x%2B+45+%29%29-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >    -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >° =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6sin%280.25%28x%2B+pi%2F4+%29%29-+9 ALIGN=MIDDLE  ALT=\"y+=+6sin%280.25%28x%2B+pi%2F4+%29%29-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Amplitude.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Period.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F0.25=2pi%2F%281%2F4%29=8pi ALIGN=MIDDLE  ALT=\"2pi%2F0.25=2pi%2F%281%2F4%29=8pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Horizontal Translation......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%2FB=45 ALIGN=MIDDLE  ALT=\"+C%2FB=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >° or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation of Midline..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-9 ALIGN=MIDDLE  ALT=\"y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=2sin%288%28x%2B+3%29%29%2B5 ALIGN=MIDDLE  ALT=\"y+=2sin%288%28x%2B+3%29%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Amplitude.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Period.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F8=pi%2F4 ALIGN=MIDDLE  ALT=\"2pi%2F8=pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Horizontal Translation......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+%2F+B+=+3 ALIGN=MIDDLE  ALT=\"C+%2F+B+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation of Midline..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=0.75sin+%284%28x-+60+%29%29 ALIGN=MIDDLE  ALT=\"y+=0.75sin+%284%28x-+60+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >° =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >radians\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=0.75sin+%284%28x-+pi%2F3+%29%29 ALIGN=MIDDLE  ALT=\"y+=0.75sin+%284%28x-+pi%2F3+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Amplitude.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.75 ALIGN=MIDDLE  ALT=\"0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Period.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F4=pi%2F2 ALIGN=MIDDLE  ALT=\"2pi%2F4=pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Horizontal Translation...... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%2FB=60 ALIGN=MIDDLE  ALT=\"+C%2FB=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation of Midline..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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