Expression 4: "a" left parenthesis, "u" , "v" , right parenthesis equals StartFraction, pi Over 2 , EndFraction left parenthesis, 1 plus cos left parenthesis, "u" , right parenthesis , right parenthesisau,v=π21+cosu
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Expression 5: "X" left parenthesis, "u" , "v" , right parenthesis equals cosine left parenthesis, "a" left parenthesis, "u" , "v" , right parenthesis , right parenthesis "X" Subscript, 0 , Baseline left parenthesis, "u" , "v" , right parenthesis minus sine left parenthesis, "a" left parenthesis, "u" , "v" , right parenthesis , right parenthesis "Y" Subscript, 0 , Baseline left parenthesis, "u" , "v" , right parenthesisXu,v=cosau,vX0u,v−sinau,vY0u,v
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Expression 6: "Y" left parenthesis, "u" , "v" , right parenthesis equals sine left parenthesis, "a" left parenthesis, "u" , "v" , right parenthesis , right parenthesis "X" Subscript, 0 , Baseline left parenthesis, "u" , "v" , right parenthesis plus cosine left parenthesis, "a" left parenthesis, "u" , "v" , right parenthesis , right parenthesis "Y" Subscript, 0 , Baseline left parenthesis, "u" , "v" , right parenthesisYu,v=sinau,vX0u,v+cosau,vY0u,v
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Expression 7: "Z" left parenthesis, "u" , "v" , right parenthesis equals 2 "R" left parenthesis, "u" , "v" , right parenthesis sine left parenthesis, "u" , right parenthesisZu,v=2Ru,vsinu
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Expression 8: left parenthesis, negative 0.4 minus "X" left parenthesis, "u" , "v" , right parenthesis , "Z" left parenthesis, "u" , "v" , right parenthesis , negative 0.3 plus "Y" left parenthesis, "u" , "v" , right parenthesis , right parenthesis−0.4−Xu,v,Zu,v,−0.3+Yu,v
