Question 961016: If sin A= -1/squareroot of 5 with A in QII, find sin 2A.
Found 3 solutions by lwsshak3, ikleyn, MathTherapy:
Answer by lwsshak3(11628)   (Show Source):
Answer by ikleyn(53875)  (Show Source):
You can put this solution on YOUR website! .
If sin A= -1/squareroot of 5 with A in QII, find sin 2A.
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As the problem is worded, printed and presented, it is self-contradictory
and describes a situation which never may happen.
In QII, sin is always non-negative, while in the problem it is given as negative value.
So, the problem is either a TRAP or a MISTAKE.
The "solution" by @lwsshak3 is wrong mathematically and dangerous
from the educational point of view, both at the same time.
The computer code which @lwsshak3 regularly uses in his practice,
is not capable to distinct nonsense from sense - it was not trained for it.
When the input is nonsense, this code regularly produces nonsense in response and deceives a reader.
@lwsshak3 does not read the output of his code and does not think on it.
In this sense, he is absolutely irresponsible, exactly as his computer code is.
Therefore, I think that an artificial intelligence will be adequate to his name
only when it will possess major human capabilities, including self-checking and
the sense of responsibility.
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Driven by my curiosity, I posted today (5/12/2026, ~ 1:40 am) this "problem"
exactly "as is" to artificial intelligence Google Overview.
It responded with the same FALSE answer and the same DEFECTIVE logic as in the post by @lwsshar3.
See this link
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
Dear Edwin - I hope you will read this.
It is how the contemporary Artificial Intelligence works
in solving trivial/routine school Math problems <<<--->>> it falls in every trap.
This case disproves ALL your arguments in your recent post.
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To be honest, one hour later I posted this problem to another artificial intelligence web-site
math-gpt.org.
This code DID RECOGNIZE the interior error in the problem, so in this aspect
it works better than Google Overview.
I don't know precisely, due to which innovation, why and how math-gpt.org is better than Google Overview.
But I see that Google Overview sometime (or regularly) uses just outdated bases of knowledge,
while more advanced AI use the most updated bases of knowledge, making re-training permanently.
It is very possible that in this case we observe precisely this situation.
In our days, versions of Artificial Intelligence are changing every 3-4 months (if not faster).
One of updates was changing/replacing once-trained AI to permanently re-trained AI to track changes
in the AI's base of knowledge. The developers of AI consider it as an important improvement:
they recognize its great importance in reflecting continuous improvements in solving
Math problems.
I also would like to note that in the area of solution school Math problems, the quality
of the relevant base of knowledge is not as high as it was expected. It happened because historically
this base of knowledge (= the base of solutions) was created by people of different qualifications -
- from high to low. Due to this reason, very often the quality of the base of knowledge in this area
does not correspond to the needs and to expectations. Therefore, cleanup and refinement of this
base remains an important task on the way to high-quality AI in this area.
The fact that the developers switch from once-trained AI to permanently re-trained AI does confirm this need.
There is another aspect of these circumstances.
Years before the era of AI, our solutions here in educational sites, were related to hundreds and thousands visitors.
But now, in the era AI, our posts, solutions and teaching do relate to millions.
Therefore, our posts and solutions (and the whole base of knowledge) should be made ideally
from the Math, logical, educational and pedagogical points of view, as well as from the common sense point of view.
In practice, it means that they should be polished permanently.
The students may not know about our efforts in improving the base of knowledge,
because they do not contact with us immediately - they do contact with AIs now.
But everything what AI knows - it knows from us, the tutors, and thanks to us and our efforts.
Everything I have written in this post is my response to Edwin's call *)
for tutors to stop working on solutions to mathematical problems on this site.
*)
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1161007.html
Edwin, we all respect your high qualification and your invaluable contribution to this forum -
I mean "all" including many visitors, tutors and the founder of this forum.
But some tutors may have different vision from yours on what to do next.
In any case, we all love you. Be happy and healthy and live long.
Answer by MathTherapy(10839)  (Show Source):
You can put this solution on YOUR website!
If sin A= -1/squareroot of 5 with A in QII, find sin 2A.
*******************************************************
This problem gives sin as negative (< 0) in the 2nd quadrant. One of the respondents confirms this, and further
states that cos is positive (> 0) in the 2nd quadrant. When did sin become negative (< 0), and cos, positive (> 0)
in the 2nd quadrant?
This is so, so RIDICULOUS and obviously WRONG. The opposite holds true, though.
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