Expression 15: "t" Subscript, "A" "y" , Baseline equals signum left parenthesis, "A" . "y" , right parenthesis left parenthesis, left brace, "A" . "y" greater than 0 : pi , 0 , right brace minus arcsin left parenthesis, StartFraction, "a" Over "A" . "y" , EndFraction , right parenthesis , right parenthesistAy=signA.yA.y>0:π,0−arcsinaA.y
equals=
negative 0.3 5 8 5 0 7 6 8 9 6 0 8−0.358507689608
15
Expression 16: "t" Subscript, "A" , Baseline equals left brace, "A" . "x" equals 0 : "t" Subscript, "A" "y" , Baseline , "t" Subscript, "A" "x" , Baseline , right bracetA=A.x=0:tAy,tAx
equals=
negative 1.0 5 5 1 1 6 4 3 8 8 3−1.05511643883
16
Expression 17: "t" Subscript, "B" "x" , Baseline equals negative signum left parenthesis, "B" . "x" , right parenthesis arc cosine left parenthesis, StartFraction, sign left parenthesis, "B" . "x" , right parenthesis times "a" Over StartRoot, "B" . "x" squared plus "B" . "y" squared , EndRoot , EndFraction , right parenthesis plus arc tangent left parenthesis, StartFraction, "B" . "y" Over "B" . "x" , EndFraction , right parenthesistBx=−signB.xarccossignB.x·aB.x2+B.y2+arctanB.yB.x
equals=
negative 2.0 7 8 1 4 4 5 1 9 0 7−2.07814451907
17
Expression 18: "t" Subscript, "B" "y" , Baseline equals negative signum left parenthesis, "B" . "y" , right parenthesis left parenthesis, left brace, "B" . "y" greater than 0 : 0 , pi , right brace minus arcsin left parenthesis, StartFraction, "a" Over "B" . "y" , EndFraction , right parenthesis , right parenthesistBy=−signB.yB.y>0:0,π−arcsinaB.y
equals=
3.7 7 0 4 6 7 5 7 9 0 83.77046757908
18
Expression 19: "t" Subscript, "B" , Baseline equals left brace, "B" . "x" equals 0 : left brace, "t" Subscript, "B" "y" , Baseline greater than "t" Subscript, "A" , Baseline : "t" Subscript, "B" "y" , Baseline , "t" Subscript, "B" "y" , Baseline plus 2 pi , right brace , left brace, "t" Subscript, "B" "x" , Baseline greater than "t" Subscript, "A" , Baseline : "t" Subscript, "B" "x" , Baseline , "t" Subscript, "B" "x" , Baseline plus 2 pi , right brace , right bracetB=B.x=0:tBy>tA:tBy,tBy+2π,tBx>tA:tBx,tBx+2π
equals=
4.2 0 5 0 4 0 7 8 8 1 14.20504078811
19
Expression 20: "b" Subscript, "A" "B" , Baseline equals StartFraction, "A" . "z" minus "B" . "z" Over left parenthesis, "r" Subscript, "A" , Baseline plus "t" Subscript, "A" , Baseline , right parenthesis minus left parenthesis, "r" Subscript, "B" , Baseline plus "t" Subscript, "B" , Baseline , right parenthesis , EndFractionbAB=A.z−B.zrA+tA−rB+tB
equals=
57.2 9 1 5 5 0 0 1 1 957.2915500119
20
Expression 21: "c" Subscript, "A" "B" , Baseline equals StartFraction, "A" . "z" left parenthesis, "r" Subscript, "B" , Baseline plus "t" Subscript, "B" , Baseline , right parenthesis minus "B" . "z" left parenthesis, "r" Subscript, "A" , Baseline plus "t" Subscript, "A" , Baseline , right parenthesis Over left parenthesis, "r" Subscript, "B" , Baseline plus "t" Subscript, "B" , Baseline , right parenthesis minus left parenthesis, "r" Subscript, "A" , Baseline plus "t" Subscript, "A" , Baseline , right parenthesis , EndFractioncAB=A.zrB+tB−B.zrA+tArB+tB−rA+tA
equals=
525.4 9 1 0 6 0 3 6 6525.491060366
21
Expression 22: "P" left parenthesis, "t" Subscript, "A" , Baseline , right parenthesis plus "r" Subscript, "A" , Baseline "t" times left parenthesis, negative "a" sin "t" Subscript, "A" , Baseline , "a" cos "t" Subscript, "A" , Baseline , "b" , right parenthesisPtA+rAt·−asintA,acostA,b
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
22
Expression 23: "P" left parenthesis, "t" Subscript, "B" , Baseline , right parenthesis plus "r" Subscript, "B" , Baseline "t" times left parenthesis, negative "a" sin "t" Subscript, "B" , Baseline , "a" cos "t" Subscript, "B" , Baseline , "b" , right parenthesisPtB+rBt·−asintB,acostB,b
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
23
Expression 24: "P" left parenthesis, "t" , right parenthesisPt
domain t Minimum: "t" Subscript, "A" , BaselinetA
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: "t" Subscript, "B" , BaselinetB
24
Length calculations
Hide this folder from students.
25
Expression 26: "L" Subscript, "A" , Baseline equals distance left parenthesis, "A" , "P" left parenthesis, "t" Subscript, "A" , Baseline , right parenthesis , right parenthesisLA=distanceA,PtA
equals=
462.7 5 7 2 0 5 9 4 4462.757205944
26
Expression 27: "L" Subscript, "B" , Baseline equals distance left parenthesis, "B" , "P" left parenthesis, "t" Subscript, "B" , Baseline , right parenthesis , right parenthesisLB=distanceB,PtB
equals=
195.9 2 3 2 2 4 0 4 7195.923224047
27
Expression 28: "L" Subscript, "H" , Baseline equals StartRoot, "a" squared plus "b" squared , EndRoot times StartAbsoluteValue, "t" Subscript, "B" , Baseline minus "t" Subscript, "A" , Baseline , EndAbsoluteValueLH=a2+b2·tB−tA
equals=
606.2 2 7 6 2 5 2 3 3606.227625233
28
Expression 29: "L" Subscript, "A" , Baseline plus "L" Subscript, "B" , Baseline plus "L" Subscript, "H" , BaselineLA+LB+LH
equals=
1264.9 0 8 0 5 5 2 21264.90805522
29
Expression 30: "L" equals StartRoot, "a" squared plus "b" squared , EndRoot times left parenthesis, StartFraction, StartRoot, "A" . "x" squared plus "A" . "y" squared minus "a" squared , EndRoot Over "a" , EndFraction plus StartFraction, StartRoot, "B" . "x" squared plus "B" . "y" squared minus "a" squared , EndRoot Over "a" , EndFraction plus "t" Subscript, "B" , Baseline minus "t" Subscript, "A" , Baseline , right parenthesisL=a2+b2·A.x2+A.y2−a2a+B.x2+B.y2−a2a+tB−tA
