Expression 61: polygon left parenthesis, left parenthesis, "l" Subscript, 1 , Baseline cos left parenthesis, "o" Subscript, 1 , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline cos left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis minus "c" Subscript, "y" , Baseline cos left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus "c" Subscript, "x" , Baseline sin left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus 1000 left brace, "c" greater than 0 : 0 , 1 , right brace , "l" Subscript, 1 , Baseline sin left parenthesis, "o" Subscript, 1 , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline sin left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus "c" Subscript, "y" , Baseline sin left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus "c" Subscript, "x" , Baseline cos left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis , right parenthesis , left parenthesis, "l" Subscript, 1 , Baseline cos left parenthesis, "o" Subscript, 1 , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline cos left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis minus left parenthesis, "c" Subscript, "y" , Baseline plus "h" Subscript, 1 , Baseline , right parenthesis cos left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus left parenthesis, "c" Subscript, "x" , Baseline plus StartFraction, "l" Subscript, 4 , Baseline Over 2 , EndFraction , right parenthesis sin left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus 1000 left brace, "c" greater than 0 : 0 , 1 , right brace , "l" Subscript, 1 , Baseline sin left parenthesis, "o" Subscript, 1 , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline sin left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus left parenthesis, "c" Subscript, "y" , Baseline plus "h" Subscript, 1 , Baseline , right parenthesis sin left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus left parenthesis, "c" Subscript, "x" , Baseline plus StartFraction, "l" Subscript, 4 , Baseline Over 2 , EndFraction , right parenthesis cos left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis , right parenthesis , left parenthesis, "l" Subscript, 1 , Baseline cos left parenthesis, "o" Subscript, 1 , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline cos left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis minus "c" Subscript, "y" , Baseline cos left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus left parenthesis, "c" Subscript, "x" , Baseline plus "l" Subscript, 4 , Baseline , right parenthesis sin left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus 1000 left brace, "c" greater than 0 : 0 , 1 , right brace , "l" Subscript, 1 , Baseline sin left parenthesis, "o" Subscript, 1 , Baseline , right parenthesis plus "l" Subscript, 2 , Baseline sin left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus "c" Subscript, "y" , Baseline sin left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis plus left parenthesis, "c" Subscript, "x" , Baseline plus "l" Subscript, 4 , Baseline , right parenthesis cos left parenthesis, StartFraction, pi Over 2 , EndFraction minus left parenthesis, "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace plus "o" Subscript, 3 , Baseline , right parenthesis , right parenthesis , right parenthesis , right parenthesispolygonl1coso1+l2coso2−cycosπ2−o2l>0:0,1+o3+cxsinπ2−o2l>0:0,1+o3+1000c>0:0,1,l1sino1+l2sino2+cysinπ2−o2l>0:0,1+o3+cxcosπ2−o2l>0:0,1+o3,l1coso1+l2coso2−cy+h1cosπ2−o2l>0:0,1+o3+cx+l42sinπ2−o2l>0:0,1+o3+1000c>0:0,1,l1sino1+l2sino2+cy+h1sinπ2−o2l>0:0,1+o3+cx+l42cosπ2−o2l>0:0,1+o3,l1coso1+l2coso2−cycosπ2−o2l>0:0,1+o3+cx+l4sinπ2−o2l>0:0,1+o3+1000c>0:0,1,l1sino1+l2sino2+cysinπ2−o2l>0:0,1+o3+cx+l4cosπ2−o2l>0:0,1+o3
61
Expression 62: "A" Subscript, 2 "c" , Baseline left parenthesis, "a" Subscript, 1 , Baseline , "a" Subscript, 2 , Baseline , right parenthesis equals StartAbsoluteValue, negative pi left brace, "a" Subscript, 1 , Baseline less than 0 : 1 , 0 , right brace plus arcsin left parenthesis, StartFraction, "l" Subscript, 2 , Baseline cos "a" Subscript, 2 , Baseline plus "c" Subscript, 4 , Baseline cos "a" Subscript, 1 , Baseline Over StartRoot, "l" squared plus "c" squared minus 2 times "l" Subscript, 2 , Baseline times "c" Subscript, 4 , Baseline times cos ( StartNestedFraction, pi NestedOver 2 , EndNestedFraction minus "a" Subscript, 2 , Baseline plus StartNestedFraction, pi NestedOver 2 , EndNestedFraction minus "a" Subscript, 1 , Baseline ) , EndRoot , EndFraction , right parenthesis , EndAbsoluteValueA2ca1,a2=−πa1<0:1,0+arcsinl2cosa2+c4cosa1l22+c24−2·l2·c4·cos(π2−a2+π2−a1)
62
Expression 63: "A" Subscript, 3 "c" , Baseline left parenthesis, "a" Subscript, 1 , Baseline , "a" Subscript, 2 , Baseline , "a" Subscript, 3 , Baseline , right parenthesis equals StartAbsoluteValue, negative pi left brace, "a" Subscript, 1 , Baseline less than 0 : 1 , 0 , right brace plus arctan left parenthesis, StartFraction, "l" Subscript, 1 , Baseline cos "a" Subscript, 3 , Baseline plus "l" Subscript, 2 , Baseline cos "a" Subscript, 2 , Baseline plus "c" Subscript, 4 , Baseline cos "a" Subscript, 1 , Baseline Over "l" Subscript, 1 , Baseline sin "a" Subscript, 3 , Baseline plus "l" Subscript, 2 , Baseline sin "a" Subscript, 2 , Baseline plus "c" Subscript, 4 , Baseline sin "a" Subscript, 1 , Baseline , EndFraction , right parenthesis , EndAbsoluteValueA3ca1,a2,a3=−πa1<0:1,0+arctanl1cosa3+l2cosa2+c4cosa1l1sina3+l2sina2+c4sina1
63
Expression 64: "c" Subscript, "t" 1 , Baseline left parenthesis, "x" , right parenthesis equals "m" Subscript, 4 , Baseline times "g" times StartRoot, left parenthesis, "l" Subscript, 1 , Baseline times cos left parenthesis, "x" , right parenthesis plus "l" Subscript, 2 , Baseline times cos left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus "c" Subscript, 4 , Baseline times cos left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared plus left parenthesis, "l" Subscript, 1 , Baseline times sin left parenthesis, "x" , right parenthesis plus "l" Subscript, 2 , Baseline times sin left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus "c" Subscript, 4 , Baseline times sin left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared , EndRoot times StartAbsoluteValue, sin ( "A" Subscript, 3 "c" , Baseline left parenthesis, left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , "o" Subscript, 2 , Baseline , "x" , right parenthesis ) , EndAbsoluteValue left brace, left parenthesis, "l" Subscript, 1 , Baseline cos "x" plus "l" Subscript, 2 , Baseline cos "o" Subscript, 2 , Baseline plus "c" Subscript, 4 , Baseline cos left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis less than 0 : negative 1 , 1 , right brace left brace, "c" greater than 0 : 1 , 0 , right bracect1x=m4·g·l1·cosx+l2·coso2+c4·coso3+o2l>0:0,12+l1·sinx+l2·sino2+c4·sino3+o2l>0:0,12·sin(A3co3+o2l>0:0,1,o2,x)l1cosx+l2coso2+c4coso3+o2l>0:0,1<0:−1,1c>0:1,0
64
Expression 65: "c" Subscript, "i" 1 , Baseline left parenthesis, "x" , right parenthesis equals "m" Subscript, 4 , Baseline times left parenthesis, left parenthesis, "l" Subscript, 1 , Baseline times cos left parenthesis, "x" , right parenthesis plus "l" Subscript, 2 , Baseline times cos left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus "c" Subscript, 4 , Baseline times cos left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared plus left parenthesis, "l" Subscript, 1 , Baseline times sin left parenthesis, "x" , right parenthesis plus "l" Subscript, 2 , Baseline times sin left parenthesis, "o" Subscript, 2 , Baseline , right parenthesis plus "c" Subscript, 4 , Baseline times sin left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared , right parenthesis left brace, "c" greater than 0 : 1 , 0 , right braceci1x=m4·l1·cosx+l2·coso2+c4·coso3+o2l>0:0,12+l1·sinx+l2·sino2+c4·sino3+o2l>0:0,12c>0:1,0
65
Expression 66: "c" Subscript, "t" 2 , Baseline left parenthesis, "x" , right parenthesis equals "m" Subscript, 4 , Baseline times "g" times StartRoot, left parenthesis, "l" Subscript, 2 , Baseline times cos left parenthesis, "x" , right parenthesis plus "c" Subscript, 4 , Baseline times cos left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared plus left parenthesis, "l" Subscript, 2 , Baseline times sin left parenthesis, "x" , right parenthesis plus "c" Subscript, 4 , Baseline times sin left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared , EndRoot times StartAbsoluteValue, sin ( "A" Subscript, 2 "c" , Baseline left parenthesis, left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , "x" , right parenthesis ) , EndAbsoluteValue times left brace, left parenthesis, "l" Subscript, 2 , Baseline cos "x" plus "c" Subscript, 4 , Baseline cos left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis less than 0 : negative 1 , 1 , right brace left brace, "c" greater than 0 : 1 , 0 , right bracect2x=m4·g·l2·cosx+c4·coso3+o2l>0:0,12+l2·sinx+c4·sino3+o2l>0:0,12·sin(A2co3+o2l>0:0,1,x)·l2cosx+c4coso3+o2l>0:0,1<0:−1,1c>0:1,0
66
Expression 67: "c" Subscript, "i" 2 , Baseline left parenthesis, "x" , right parenthesis equals "m" Subscript, 4 , Baseline times left parenthesis, left parenthesis, "l" Subscript, 2 , Baseline times cos left parenthesis, "x" , right parenthesis plus "c" Subscript, 4 , Baseline times cos left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared plus left parenthesis, "l" Subscript, 2 , Baseline times sin left parenthesis, "x" , right parenthesis plus "c" Subscript, 4 , Baseline times sin left parenthesis, "o" Subscript, 3 , Baseline plus "o" Subscript, 2 , Baseline left brace, "l" greater than 0 : 0 , 1 , right brace , right parenthesis , right parenthesis squared , right parenthesis left brace, "c" greater than 0 : 1 , 0 , right braceci2x=m4·l2·cosx+c4·coso3+o2l>0:0,12+l2·sinx+c4·sino3+o2l>0:0,12c>0:1,0
67
Expression 68: "c" Subscript, "t" 3 , Baseline left parenthesis, "x" , right parenthesis equals "m" Subscript, 4 , Baseline times "g" times "c" Subscript, 4 , Baseline times StartAbsoluteValue, sin ( "A" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis ) , EndAbsoluteValue times left brace, StartFraction, pi Over 2 , EndFraction less than "x" less than StartFraction, 3 pi Over 2 , EndFraction : negative 1 , 1 , right brace left brace, "c" greater than 0 : 1 , 0 , right bracect3x=m4·g·c4·sin(A1x)·π2<x<3π2:−1,1c>0:1,0
68
Expression 69: "c" Subscript, "i" 3 , Baseline left parenthesis, "x" , right parenthesis equals "m" Subscript, 4 , Baseline times "c" squared left brace, "c" greater than 0 : 1 , 0 , right braceci3x=m4·c24c>0:1,0
