Expression 3: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" less than or equal to "x" less than or equal to "t" plus StartFraction, pi Over 2 , EndFraction : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" plus pi : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" plus pi less than "x" less than "t" plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" plus 2 pi : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , right brace Has graph. To audio trace, press ALT+T.fx=t≤x≤t+π2:sinxcosx−t+sinx−t,t+π2<x<t+π:−sinxcosx−t−sinx−t,t+π<x<t+3π2:−sinxcosx−t+sinx−t,t+3π2<x<t+2π:sinxcosx−t−sinx−t
3
Expression 4: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" minus 2 pi less than or equal to "x" less than or equal to "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" minus 2 pi plus pi : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" minus 2 pi plus pi less than "x" less than "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" minus 2 pi plus 2 pi : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , right brace Has graph. To audio trace, press ALT+T.fx=t−2π≤x≤t−2π+π2:sinxcosx−t+sinx−t,t−2π+π2<x<t−2π+π:−sinxcosx−t−sinx−t,t−2π+π<x<t−2π+3π2:−sinxcosx−t+sinx−t,t−2π+3π2<x<t−2π+2π:sinxcosx−t−sinx−t
4
Expression 5: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" less than or equal to "x" less than or equal to "t" plus StartFraction, pi Over 2 , EndFraction : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" plus pi : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" plus pi less than "x" less than "t" plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" plus 2 pi : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , right brace Has graph. To audio trace, press ALT+T.fx=t≤x≤t+π2:cosx2sinx−t+π4,t+π2<x<t+π:cosx2sinx−t−π4,t+π<x<t+3π2:−cosx2sinx−t+π4,t+3π2<x<t+2π:−cosx2sinx−t−π4
5
Expression 6: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" minus 2 pi less than or equal to "x" less than or equal to "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" minus pi : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" minus pi less than "x" less than "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , right brace Has graph. To audio trace, press ALT+T.fx=t−2π≤x≤t−2π+π2:cosx2sinx−t+π4,t−2π+π2<x<t−π:cosx2sinx−t−π4,t−π<x<t−2π+3π2:−cosx2sinx−t+π4,t−2π+3π2<x<t:−cosx2sinx−t−π4
