document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189597>Question 1189597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sinθ+cosθ= 1/√2 , then which of the following is true (A) θ can be in Quadrant I (B) θ must be in Quadrant II or IV (C) must be in Quadrant I or IV (D) θ can be in Quadrant I, II, or III (E) none of the above is correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821003 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=821003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29%2Bcos%28theta%29=+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29%2Bcos%28theta%29=+1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2+%28theta%29+%2B+2sin%28theta%29cos%28theta%29+%2B+cos%5E2+%28theta%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"sin%5E2+%28theta%29+%2B+2sin%28theta%29cos%28theta%29+%2B+cos%5E2+%28theta%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28theta%29cos%28theta%29=+sin+%282theta%29+ ALIGN=MIDDLE  ALT=\"2sin%28theta%29cos%28theta%29=+sin+%282theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+sin+%282theta%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"1+%2B+sin+%282theta%29+=+1%2F2\"   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=sin+%282theta%29+=+1%2F2-1 ALIGN=MIDDLE  ALT=\"sin+%282theta%29+=+1%2F2-1\"   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=sin+%282theta%29+=+-1%2F2+ ALIGN=MIDDLE  ALT=\"sin+%282theta%29+=+-1%2F2+\"   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=2theta+=+210 ALIGN=MIDDLE  ALT=\"2theta+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" >°  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2theta+=+330 ALIGN=MIDDLE  ALT=\"2theta+=+330\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=+105 ALIGN=MIDDLE  ALT=\"theta=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >° or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=+165 ALIGN=MIDDLE  ALT=\"theta=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "but the period of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282theta%29 ALIGN=MIDDLE  ALT=\"sin+%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, so other solutions would be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=105%2B180+=+285 ALIGN=MIDDLE  ALT=\"105%2B180+=+285\"   DISABLED_style= \"max-width:90%; height:auto;\" >° and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2B180+=+345 ALIGN=MIDDLE  ALT=\"165%2B180+=+345\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "BUT, since we squared our equation, all answers must be verifies\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+105 ALIGN=MIDDLE  ALT=\"theta+=+105\"   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=sin%28105%29+%2B+cos%28105%29+=+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sin%28105%29+%2B+cos%28105%29+=+1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+165 ALIGN=MIDDLE  ALT=\"theta+=+165\"   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=sin+%28165+%29%2B+cos+%28165%29 ALIGN=MIDDLE  ALT=\"sin+%28165+%29%2B+cos+%28165%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ≠ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+285 ALIGN=MIDDLE  ALT=\"theta+=+285\"   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=sin%28285%29%2Bcos%28285%29+ ALIGN=MIDDLE  ALT=\"sin%28285%29%2Bcos%28285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ≠ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=+345 ALIGN=MIDDLE  ALT=\"theta=+345\"   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=sin+%28345%29%2Bcos%28345%29++=+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sin+%28345%29%2Bcos%28345%29++=+1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+105 ALIGN=MIDDLE  ALT=\"theta+=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >° in quad II\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+345 ALIGN=MIDDLE  ALT=\"theta+=+345\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, which is in quad IV\r<BR>\n" );
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document.write( "answer: (B) θ must be in Quadrant II or IV\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );