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Re: a history of regents exam errors
Posted:
Jul 1, 2011 9:58 AM
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Does anyone have a link to that article?
Eileen Lane
Union-Endicott H.S.
Math Dept.
>>> Evan Romer <evanromer@gmail.com> 07/01/11 9:50 AM >>>
I agree that cos^-1 represents the inverse trig function (and the
glossary says so also). So its range should be [0,pi].
But even if you grant that cos^-1 represents the inverse of cos, not
necessarily the inverse function of cos, then the range should be all
real numbers.
So under either interpretation of cos^-1, there is no correct choice
given. There is no interpretation of cos^-1 for which the range is
[0,2pi].
Evan Romer
Susquehanna Valley HS
On Jun 30, 2011, at 8:08AM, Nick B wrote:
> What about #19 this year, with no correct answer?
>
> There was a Newsday article published about the errors on the test,
> and the focus was on #19. Some had commented on the online version
> of the article saying that inverse cosine doesn't have to be a
> function; however, we can go to the NYSDOE Glossary for grades 9-12
> to see that assertion is false, even according to the state:
>
>
http://www.jmap.org/JMAP/SupportFiles/NYS-NYCDOEDocuments/Math/Glossaries/NYSDOE_Glossary_Grades_9-12.pdf
>
> (Page 42) inverse trigonometric functions (A2T) Given the value of a
> trigonometric function for an angle ?, the inverse trigonometric
> function outputs the measure of angle ?. The inverses of the six
> basic trigonometric functions are written as sin-1, cos-1, tan-1,
> csc-1, sec-1, and cot-1.
>
> While that is a lousy definition, the state is clearly defining the
> ^-1 notation as the inverse function. None of the choices in #19 is
> a function. I happen to know the people at Stony Brook University
> in the Newsday article personally and ALL are fantastic
> mathematicians and teachers and would not lead us astray.
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