[UEB Maths] First sample
Phippen, Stephen
uebmaths@nbp.org
Mon, 12 Sep 2005 14:50:12 +0100
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To: UEB Maths Committee
From: Stephen Phippen
Date: 12 September 2005
Here is a first sample illustrating the suggested rules for dealing with =
word fragments (such as functions). This sample only contains the usual =
trigonometric functions; I will do a second sample with some other types =
of word fragments when I find some example text.
The sample has been done in two forms according to the proposed wording =
of the rule which gives the option. The first uses the word indicator =
method (as well as abbreviated forms for sin, cos and tan); then the =
second uses the method of spacing the word fragments.
I have included the DBT file as an attachment, as well as a jpeg image =
file of the original print in case it is useful to refer to.
I noted down a number of debatable points on working through this, which =
may need documenting one way or another:
1. For set out equations, I have included the equation numbers within =
the grade 1 passage mode indicators, rather than outside.
2. For punctuation marks following equations, I have included them =
within the grade 1 passage for set out equations, but placed them after =
the grade 1 terminator for equations embedded in ordinary text.
3. In the first version I have used just the single grade 1 indicator =
before cases such as cos x or cos squared x within ordinary text. In the =
first case I argued that the dot 3 before the x could only have its =
meaning as a terminator to the word fragment, and in the second case I =
think we can similarly say that the dots 26 sign ending the word =
fragment can only be read with grade 1 meaning, i.e. as a subscript =
sign.
4. In "Example 1" I closed the grade 1 passage at the end of the =
paragraph, and restarted it again for the immediately following set out =
equation, rather than just continuing the passage.
5. Where the original print specially starts a new line with an equals =
sign, I have done the same in the braille, but started at the runover =
margin, rather than starting in the cell I would use for a new set out =
equation.
6. Where "cos" and "sin" appear within an ordinary sentence, I have used =
the word indicator method in the first version, but treated them as =
ordinary words in the second version.
7. In the second version I haven't spaced cos squared or sin squared =
from a following argument. See, for example, example 1, where we have =
sin x + sin squared x (hence the spacing looks a bit unbalanced).
8. In the second version I have included a space before the word =
fragment in cases like 2 cos x. The space is necessary to avoid the "c" =
being misread as a number. But for consistency I have done the same for =
2 sin x.
----------
#A
,,EX]CISE #H
"<^W 9DICATOR ME?OD">
,ID5TITIES4
,"! >E F\R IMPORTANT ID5TITIES :
EXI/ 2T ! RATIOS4
,! F/ ( ^! FOLL[S F ! DEF9I;N (
TANG5T1
;;;"<I"> *T'X "7 (*S'X./*C'X);'
,IF ;,P IS ! PO9T ON ! CIRCLE ( UNIT
RADIUS S* T ;;;X,O":,P "7 X;'1 !N !
COORD9ATES ( ;,P >E
;;;"<*C'X1 *S'X">;'4
,B
;;;,,NO9#B"6,,PN9#B "7 ,,PO9#B1;'
OR
;;;"<II"> *C9#BX"6*S9#BX "7 #A;'
,DIVIDE EQUA;N "<II"> BY ;*C9#BX &
;;;"<III"> #A"6*T9#BX
"7 *SEC9#BX;'
,DIVIDE EQUA;N "<II"> BY ;*S9#BX &
;;;"<IV"> *COT9#BX"6#A
"7 *COSEC9#BX;'
,^! =3DMULAE >E ALL TRUE =3D ANGLES (
=0C #B
ANY MAGNITUDE4
.1EXAMPLE .1#A4 ,PROVE ;;;"<*C'X
"6*S'X">9#B"6"<*C'X"-*S'X">9#B
"7 #B;'4
;;;"<*C'X"6*S'X">9#B"6"<*C'X
"-*S'X">9#B
"7 *C9#BX"6#B*C'X*S'X"6*S9#BX
"6*C9#BX"-#B*C'X*S'X"6*S9#BX
"7 #B"<*C9#BX"6*S9#BX">
"7 #B,4;'
.1EXAMPLE .1#B4 ,PROVE T ;;;*COT'X
"6*T'X "7 *SEC'X*COSEC'X;'4
"<9 PROV+ ID5TITIES1 X IS (T5 A GD
PLAN TO EXPRESS ALL QUANTITIES 9 T]MS
( ;*C & ;*S4">
;;;*COT'X"6*T'X "7 (*C'X./*S'X)
"6(*S'X./*C'X)
"7 (*C9#BX"6*S9#BX./*C'X*S'X)
"7 (#A./*C'X*S'X)
"7 *SEC'X*COSEC'X4;'
.1EXAMPLE .1#C4 ,F9D ALL VALUES ( ;X
2T #J^J & #CFJ^J : SATISFY ! EQUA;N
;;;#E*C'X "7 #B*S'X4;'
,DIVIDE BO? SIDES ( ! EQUA;N BY
=0C #C
;*C'X
;;;#E "7 #B*T'X4
,* *T'X "7 #B4E4;'
;X "7 #FH^J#AB7 IS "O SOLU;N4 ;*T'X
IS POSITIVE 9 ! F/ & ?IRD QUADRANTS &
S ! ONLY O!R POSSI# SOLU;N IS ! ANGLE
9 ! ?IRD QUADRANT : MAKES #FH^J#AB7 )
! ;X-AXIS1 I4E4
#AHJ^J"6#FH^J#AB7 "7 #BDH^J#AB74
;X "7 #FH^J#AB7 OR #BDH^J#AB74
"333333333333
=0C #D
=20
,,EX]CISE #H
"<SPAC+ ME?OD">
,ID5TITIES4
,"! >E F\R IMPORTANT ID5TITIES :
EXI/ 2T ! RATIOS4
,! F/ ( ^! FOLL[S F ! DEF9I;N (
TANG5T1
;;;"<I"> TAN X "7 (SIN X./COS X);'
,IF ;,P IS ! PO9T ON ! CIRCLE ( UNIT
RADIUS S* T ;;;X,O":,P "7 X;'1 !N !
COORD9ATES ( ;,P >E
;;;"<COS X1 SIN X">;'4
,B
;;;,,NO9#B"6,,PN9#B "7 ,,PO9#B1;'
OR
;;;"<II"> COS9#BX"6SIN9#BX "7 #A;'
,DIVIDE EQUA;N "<II"> BY COS;9#BX &
;;;"<III"> #A"6TAN9#BX
"7 SEC9#BX;'
,DIVIDE EQUA;N "<II"> BY SIN;9#BX &
;;;"<IV"> COT9#BX"6#A
"7 *COSEC9#BX;'
,^! =3DMULAE >E ALL TRUE =3D ANGLES (
=0C #E
ANY MAGNITUDE4
.1EXAMPLE .1#A4 ,PROVE ;;;"<COS X
"6SIN X">9#B"6"<COS X"-SIN X">9#B
"7 #B;'4
;;;"<COS X"6SIN X">9#B"6"<COS X
"-SIN X">9#B
"7 COS9#BX"6#B COS X SIN X
"6SIN9#BX"6COS9#BX"-#B COS X
SIN X"6SIN9#BX
"7 #B"<COS9#BX"6SIN9#BX">
"7 #B,4;'
.1EXAMPLE .1#B4 ,PROVE T ;;;COT X
"6TAN X "7 SEC X COSEC X;'4
"<9 PROV+ ID5TITIES1 X IS (T5 A GD
PLAN TO EXPRESS ALL QUANTITIES 9 T]MS
( COS & S94">
;;;COT X"6TAN X "7 (COS X./SIN X)
"6(SIN X./COS X)
"7 (COS9#BX"6SIN9#BX./COS X
SIN X)
"7 (#A./COS X SIN X) "7 SEC X
COSEC X4;'
.1EXAMPLE .1#C4 ,F9D ALL VALUES ( ;X
2T #J^J & #CFJ^J : SATISFY ! EQUA;N
=0C #F
;;;#E COS X "7 #B SIN X4;'
,DIVIDE BO? SIDES ( ! EQUA;N BY COS
;X
;;;#E "7 #B TAN X4
,* TAN X "7 #B4E4;'
;X "7 #FH^J#AB7 IS "O SOLU;N4 TAN ;X
IS POSITIVE 9 ! F/ & ?IRD QUADRANTS &
S ! ONLY O!R POSSI# SOLU;N IS ! ANGLE
9 ! ?IRD QUADRANT : MAKES #FH^J#AB7 )
! ;X-AXIS1 I4E4
#AHJ^J"6#FH^J#AB7 "7 #BDH^J#AB74
;X "7 #FH^J#AB7 OR #BDH^J#AB74
"333333333333
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