document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=961016>Question 961016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin A= -1/squareroot of 5 with A in QII, find sin 2A. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854562 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53875)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "If sin A= -1/squareroot of 5 with A in QII, find sin 2A.<BR>\n" );
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document.write( "As the problem is worded, printed and presented, it is self-contradictory<BR>\n" );
document.write( "and describes a situation which never may happen.<BR>\n" );
document.write( "In QII, sin is always non-negative, while in the problem it is given as negative value.\r<BR>\n" );
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document.write( "So, the problem is either a TRAP or a MISTAKE.<BR>\n" );
document.write( "The \"solution\" by @lwsshak3 is wrong mathematically and dangerous <BR>\n" );
document.write( "from the educational point of view, both at the same time.\r<BR>\n" );
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document.write( "The computer code which @lwsshak3 regularly uses in his practice, <BR>\n" );
document.write( "is not capable to distinct nonsense from sense - it was not trained for it.<BR>\n" );
document.write( "When the input is nonsense, this code regularly produces nonsense in response and deceives a reader.\r<BR>\n" );
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document.write( "@lwsshak3 does not read the output of his code and does not think on it.<BR>\n" );
document.write( "In this sense, he is absolutely irresponsible, exactly as his computer code is.\r<BR>\n" );
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document.write( "Therefore, I think that an artificial intelligence will be adequate to his name<BR>\n" );
document.write( "only when it will possess major human capabilities, including self-checking and <BR>\n" );
document.write( "the sense of responsibility.\r<BR>\n" );
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document.write( "Driven by my curiosity, I posted today (5/12/2026, ~ 1:40 am) this \"problem\" <BR>\n" );
document.write( "exactly \"as is\" to artificial intelligence Google Overview.\r<BR>\n" );
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document.write( "It responded with the same FALSE answer and the same DEFECTIVE logic as in the post by @lwsshar3.\r<BR>\n" );
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document.write( "See this link\r<BR>\n" );
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document.write( "https://www.google.com/search?q=If+sin+A%3D+-1%2Fsquareroot+of+5+with+A+in+QII%2C+find+sin+2A.&rlz=1C1CHBF_enUS1071US1071&oq=If+sin+A%3D+-1%2Fsquareroot+of+5+with+A+in+QII%2C+find+sin+2A.&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIHCAEQIRiPAjIHCAIQIRiPAtIBCTIwODRqMGoxNagCCLACAfEFy4JCYaOJAy4&sourceid=chrome&ie=UTF-8\r<BR>\n" );
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document.write( "Dear Edwin - I hope you will read this.\r<BR>\n" );
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document.write( "It is how the contemporary Artificial Intelligence works <BR>\n" );
document.write( "in solving trivial/routine school Math problems <<<--->>> it falls in every trap.\r<BR>\n" );
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document.write( "This case disproves ALL your arguments in your recent post.\r<BR>\n" );
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document.write( "To be honest, one hour later I posted this problem to another artificial intelligence web-site<BR>\n" );
document.write( "math-gpt.org.\r<BR>\n" );
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document.write( "This code DID RECOGNIZE the interior error in the problem, so in this aspect <BR>\n" );
document.write( "it works better than Google Overview.\r<BR>\n" );
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document.write( "I don't know precisely, due to which innovation, why and how math-gpt.org is better than Google Overview.\r<BR>\n" );
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document.write( "But I see that Google Overview sometime (or regularly) uses just outdated bases of knowledge,<BR>\n" );
document.write( "while more advanced AI use the most updated bases of knowledge, making re-training permanently.<BR>\n" );
document.write( "It is very possible that in this case we observe precisely this situation.\r<BR>\n" );
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document.write( "In our days, versions of Artificial Intelligence are changing every 3-4 months (if not faster).<BR>\n" );
document.write( "One of updates was changing/replacing once-trained AI to permanently re-trained AI to track changes <BR>\n" );
document.write( "in the AI's base of knowledge. The developers of AI consider it as an important improvement:<BR>\n" );
document.write( "they recognize its great importance in reflecting continuous improvements in solving<BR>\n" );
document.write( "Math problems.\r<BR>\n" );
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document.write( "I also would like to note that in the area of solution school Math problems, the quality <BR>\n" );
document.write( "of the relevant base of knowledge is not as high as it was expected. It happened because historically <BR>\n" );
document.write( "this base of knowledge (= the base of solutions) was created by people of different qualifications - <BR>\n" );
document.write( "- from high to low. Due to this reason, very often the quality of the base of knowledge in this area <BR>\n" );
document.write( "does not correspond to the needs and to expectations. Therefore, cleanup and refinement of this <BR>\n" );
document.write( "base remains an important task on the way to high-quality AI in this area.\r<BR>\n" );
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document.write( "The fact that the developers switch from once-trained AI to permanently re-trained AI does confirm this need. \r<BR>\n" );
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document.write( "There is another aspect of these circumstances.\r<BR>\n" );
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document.write( "Years before the era of AI, our solutions here in educational sites, were related to hundreds and thousands visitors.<BR>\n" );
document.write( "But now, in the era AI, our posts, solutions and teaching do relate to millions.<BR>\n" );
document.write( "Therefore, our posts and solutions (and the whole base of knowledge) should be made ideally <BR>\n" );
document.write( "from the Math, logical, educational and pedagogical points of view, as well as from the common sense point of view.<BR>\n" );
document.write( "In practice, it means that they should be polished permanently.\r<BR>\n" );
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document.write( "The students may not know about our efforts in improving the base of knowledge, <BR>\n" );
document.write( "because they do not contact with us immediately - they do contact with AIs now.\r<BR>\n" );
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document.write( "But everything what AI knows - it knows from us, the tutors, and thanks to us and our efforts.\r<BR>\n" );
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document.write( "Everything I have written in this post is my response to Edwin's call *) <BR>\n" );
document.write( "for tutors to stop working on solutions to mathematical problems on this site.\r<BR>\n" );
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document.write( "*)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1161007.html\r<BR>\n" );
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document.write( "Edwin, we all respect your high qualification and your invaluable contribution to this forum - <BR>\n" );
document.write( "I mean \"all\" including many visitors, tutors and the founder of this forum.\r<BR>\n" );
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document.write( "But some tutors may have different vision from yours on what to do next.\r<BR>\n" );
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document.write( "In any case, we all love you. Be happy and healthy and live long.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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