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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Quiz 8 MCS 320 Friday 14 M
arch 2003" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "1
. Give the Maple command(s) to verify the following trigonometric iden
tity:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 
"trigidty := cos(x) + cos(y) = 2*cos(x/2+y/2)*cos(x/2-y/2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%)trigidtyG/,&-%$cosG6#%\"xG\"\"\"-F(6#%\"y
GF+,$*&-F(6#,&F*#F+\"\"#*&F4F+F.F+F+F+-F(6#,&F*F4*&#F+F5F+F.F+!\"\"F+F
5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "ANSWER:" }{MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Here is the shortest way:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "trigsub
s(lhs(trigidty));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#,$*&-%$cosG6#,&
%\"xG#\"\"\"\"\"#*&F+F,%\"yGF,F,F,-F'6#,&F*F+*&#F,F-F,F/F,!\"\"F,F-" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "We can also start with the right
 hand side:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 23 "combine(rhs(trigidty));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-
%$cosG6#%\"xG\"\"\"-F%6#%\"yGF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
39 "But the random point test is also good:" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "a := evalf(rand()/10^12); b \+
:= evalf(rand()/10^12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$\"+
\"p'>uU!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"+Lp56K!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subs(x=a,y=b,trigidty);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%$cosG6#$\"+\"p'>uU!#5\"\"\"-F&6#$
\"+Lp56KF*F+,$*&-F&6#$\"+7=lUPF*F+-F&6#$\"*!)[aJ&F*F+\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/$\"+LQ#*e=!\"*F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
87 "2. One mile is 1.6 km. Give the extension to convert which enables
 a session like this:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 19 "  [> d := 23*miles:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 19 "  [> convert(d,km);" }}{PARA 0 "" 0 "" {TEXT -1 68 "   \+
                                                          36.8 km" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "`conver
t/km` := proc(d)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "   return op(1,
d)*1.6*km:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%+convert/kmGf*6#%\"dG6\"F(F(O,$*&-%#opG6$\"\"
\"9$F/%#kmGF/$\"#;!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "d := 23*miles;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG,$%&mile
sG\"#B" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Notice, we must select \+
the first operand of the expression." }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(1,d);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#B" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "conv
ert(d,km);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#kmG$\"$o$!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "19 0 0" 0 }
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