document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395390>Question 395390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, please help me solve this problem:\r<BR>\n" );
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document.write( "Is this true of false: If alpha and beta are in standard position and are coterminal, then cos alpha must equal cos beta. \r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280645 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall that coterminal angles x and y are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=360k%2Bx ALIGN=MIDDLE  ALT=\"y=360k%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some integer k. For example, say x=20 and k=2, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=360%2A2%2B20=720%2B20=740 ALIGN=MIDDLE  ALT=\"y=360%2A2%2B20=720%2B20=740\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So x=20 and y=740 are coterminal angles.\r<BR>\n" );
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document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta ALIGN=MIDDLE  ALT=\"beta\"   DISABLED_style= \"max-width:90%; height:auto;\" > are coterminal angles, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta=360k%2Balpha ALIGN=MIDDLE  ALT=\"beta=360k%2Balpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now take the cosine of both sides to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=cos%28360k%2Balpha%29 ALIGN=MIDDLE  ALT=\"cos%28beta%29=cos%28360k%2Balpha%29\"   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=cos%28beta%29=cos%28360k%29cos%28alpha%29-sin%28360k%29sin%28alpha%29 ALIGN=MIDDLE  ALT=\"cos%28beta%29=cos%28360k%29cos%28alpha%29-sin%28360k%29sin%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand the right side.\r<BR>\n" );
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document.write( "Note: since k is an integer (ie whole number), this means that numbers of the form 360k are: 360, 720, ... So this means that the cosine of 360k is 1. Why? We can easily show that cos(360*2)=cos(360+360)=cos(360)cos(360)-sin(360)sin(360)=1*1-0*0=1. So cos(360*2)=cos(360). We can extend this infinitely, which means that cos(360k)=1. The same idea applies to sine as well. So sin(360k)=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=1%2Acos%28alpha%29-0%2Asin%28alpha%29 ALIGN=MIDDLE  ALT=\"cos%28beta%29=1%2Acos%28alpha%29-0%2Asin%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the cosine and sine of 360k to get 1 and 0 (see explanation above)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=cos%28alpha%29-0 ALIGN=MIDDLE  ALT=\"cos%28beta%29=cos%28alpha%29-0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=cos%28alpha%29 ALIGN=MIDDLE  ALT=\"cos%28beta%29=cos%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So because we've shown that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=cos%28alpha%29 ALIGN=MIDDLE  ALT=\"cos%28beta%29=cos%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the statement is true.\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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