Expression 7: left parenthesis, StartFraction, left parenthesis, left parenthesis, 6cos "t" plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, 2 plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, 6cos "t" plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, 2 plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , StartFraction, 6sin "t" plus "b" Over StartRoot, left parenthesis, 6cos "t" plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, 2 plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , right parenthesis6cost+acos(θ1)−2+csin(θ1)6cost+asin(θ1)+2+ccos(θ1),6sint+b6cost+asin(θ1)+2+ccos(θ1)
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 2 pi2π
7
Hidden Label: left parenthesis, StartFraction, left parenthesis, left parenthesis, "x" Subscript, 1 , Baseline plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, "z" Subscript, 1 , Baseline plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 1 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 1 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction left brace, StartAbsoluteValue, StartFraction, left parenthesis, left parenthesis, "x" Subscript, 1 , Baseline plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, "z" Subscript, 1 , Baseline plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 1 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 1 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , EndAbsoluteValue less than or equal to 20 , right brace , StartFraction, left parenthesis, "y" Subscript, 1 , Baseline plus "b" , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 1 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 1 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction left brace, StartAbsoluteValue, StartFraction, left parenthesis, "y" Subscript, 1 , Baseline plus "b" , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 1 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 1 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , EndAbsoluteValue less than or equal to 20 , right brace , right parenthesisx1+acos(θ1)−z1+csin(θ1)x1+asin(θ1)+z1+ccos(θ1)x1+acos(θ1)−z1+csin(θ1)x1+asin(θ1)+z1+ccos(θ1)≤20,y1+bx1+asin(θ1)+z1+ccos(θ1)y1+bx1+asin(θ1)+z1+ccos(θ1)≤20
Label
equals=
left parenthesis, 5.4 2 3 , negative 1.8 9 8 , right parenthesis5.423,−1.898
left parenthesis, 5.4 9 3 , negative 2.8 9 , right parenthesis5.493,−2.89
8
Hidden Label: left parenthesis, StartFraction, left parenthesis, left parenthesis, "x" Subscript, 2 , Baseline plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, "z" Subscript, 2 , Baseline plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 2 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 2 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction left brace, StartAbsoluteValue, StartFraction, left parenthesis, left parenthesis, "x" Subscript, 2 , Baseline plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, "z" Subscript, 2 , Baseline plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 2 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 2 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , EndAbsoluteValue less than or equal to 20 , right brace , StartFraction, left parenthesis, "y" Subscript, 2 , Baseline plus "b" , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 2 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 2 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction left brace, StartAbsoluteValue, StartFraction, left parenthesis, "y" Subscript, 2 , Baseline plus "b" , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 2 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 2 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , EndAbsoluteValue less than or equal to 20 , right brace , right parenthesisx2+acos(θ1)−z2+csin(θ1)x2+asin(θ1)+z2+ccos(θ1)x2+acos(θ1)−z2+csin(θ1)x2+asin(θ1)+z2+ccos(θ1)≤20,y2+bx2+asin(θ1)+z2+ccos(θ1)y2+bx2+asin(θ1)+z2+ccos(θ1)≤20
Label
equals=
left parenthesis, 5.4 2 3 , negative 1.8 9 8 , right parenthesis5.423,−1.898
left parenthesis, 5.3 9 6 , negative 2.4 4 , right parenthesis5.396,−2.44
9
Hidden Label: left parenthesis, StartFraction, left parenthesis, left parenthesis, "x" Subscript, 3 , Baseline plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, "z" Subscript, 3 , Baseline plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 3 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 3 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction left brace, StartAbsoluteValue, StartFraction, left parenthesis, left parenthesis, "x" Subscript, 3 , Baseline plus "a" , right parenthesis cos ( theta Subscript, 1 , Baseline ) minus left parenthesis, "z" Subscript, 3 , Baseline plus "c" , right parenthesis sin ( theta Subscript, 1 , Baseline ) , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 3 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 3 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , EndAbsoluteValue less than or equal to 20 , right brace , StartFraction, left parenthesis, "y" Subscript, 3 , Baseline plus "b" , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 3 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 3 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction left brace, StartAbsoluteValue, StartFraction, left parenthesis, "y" Subscript, 3 , Baseline plus "b" , right parenthesis Over StartRoot, left parenthesis, "x" Subscript, 3 , Baseline plus "a" , right parenthesis sin ( theta Subscript, 1 , Baseline ) plus left parenthesis, "z" Subscript, 3 , Baseline plus "c" , right parenthesis cos ( theta Subscript, 1 , Baseline ) , EndRoot , EndFraction , EndAbsoluteValue less than or equal to 20 , right brace , right parenthesisx3+acos(θ1)−z3+csin(θ1)x3+asin(θ1)+z3+ccos(θ1)x3+acos(θ1)−z3+csin(θ1)x3+asin(θ1)+z3+ccos(θ1)≤20,y3+bx3+asin(θ1)+z3+ccos(θ1)y3+bx3+asin(θ1)+z3+ccos(θ1)≤20
Label
equals=
left parenthesis, 5.4 2 3 , negative 1.8 9 8 , right parenthesis5.423,−1.898
left parenthesis, 6.0 6 3 , negative 1.2 6 , right parenthesis6.063,−1.26
10
"x" Subscript, 1 , Baselinex1
"y" Subscript, 1 , Baseliney1
"z" Subscript, 1 , Baselinez1
00
00
22
r1c4:
5.5cosine left parenthesis, negative "t" Subscript, 1 , Baseline pi 2 plus StartFraction, pi Over 2 , EndFraction , right parenthesis5.5cos−t1π2+π2
5.5sine left parenthesis, negative "t" Subscript, 1 , Baseline pi 2 plus StartFraction, pi Over 2 , EndFraction , right parenthesis5.5sin−t1π2+π2
22
r2c4:
r3c4:
11
"x" Subscript, 2 , Baselinex2
"y" Subscript, 2 , Baseliney2
"z" Subscript, 2 , Baselinez2
00
00
22
r1c4:
3cosine left parenthesis, StartFraction, negative "t" Subscript, 1 , Baseline pi Over 30 , EndFraction plus StartFraction, pi Over 2 , EndFraction , right parenthesis3cos−t1π30+π2
3sine left parenthesis, StartFraction, negative "t" Subscript, 1 , Baseline pi Over 30 , EndFraction plus StartFraction, pi Over 2 , EndFraction , right parenthesis3sin−t1π30+π2
22
r2c4:
r3c4:
12
"x" Subscript, 3 , Baselinex3
"y" Subscript, 3 , Baseliney3
"z" Subscript, 3 , Baselinez3
00
00
22
r1c4:
5cosine left parenthesis, StartFraction, negative "t" Subscript, 1 , Baseline pi Over 1800 , EndFraction plus StartFraction, pi Over 2 , EndFraction , right parenthesis5cos−t1π1800+π2
5sine left parenthesis, StartFraction, negative "t" Subscript, 1 , Baseline pi Over 1800 , EndFraction plus StartFraction, pi Over 2 , EndFraction , right parenthesis5sin−t1π1800+π2