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sin x sin y
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;3D39g&Vhi287F5jDE7F/AD'7474D):3DEGkJ59Y-Y11J242413BFDE9lT 19:24/.*E9Y:3@V>U2F2Z@>U2>-0/A75728@e74DED+<DE=FGD'D39
:3@E7F/H2>:J7569m</./.=F28@E-0@E,.,A@07F5:3@W</.928DE:1;3DEDVB4DE9m5n2428@N28D'74D3IiD3=4;'*E:3@V>=4@'724X'9g&R/./.=F=8@
T 19:U28/.*E,.,.5
sin x sin y
2ZDE74D3IiDE=F;'*':3@>=8@E728XJ&(+*':'5/.,.5o-Y>'XU7j28@'7F74@W56=F/g*'<J24/.*'/H28DJ&pJ&qRKDE=8D3-0524=4/.-Y1*?kJ*U7F74DlD39952F241$567F/H2>?7K28DE=F:'*'/r2428D'DL57F/r2>?72Z@L:3@>?=4@'728@C2ZD3/</.99D'7I
28DJsJB*'9:3D[-$@'@E=F/H24245,.56;3@32l:E*?*'=4kJ/.9DED328/r2Y=F/./.<<1;3D32qB*U728DE/.9t<D3=8DE-W524=4/A728DJ&^)@E,HI
,AD3/.9569m*E9567F/.-05=4:/.:?7F/g:3@V>=4@
( x(t) = t sin t
y(t) = t cos t , t ∈ [0, 2π]
RS/./.=4=4@N2Z@3-$@W<DE=4DE-05n28=F/.-Y1*?kJ*U7474DW*E,.56;3DW:3@>=8@?&(+*E:'56/H,.5o56=F/g*'<J24/.*'/H28DJ&
u &qR/./.=F=8@l5=4/.,ADE/A7/ADl:?1J;?/ADl:E*',.-0/.1,.*324245/A7F5728Dl<D3=8DE-W524=4/.-Y1*?kJ*U747FDYDE995n28172ZDl:3@>UI
=4@'728@
x(t) = sin t y(t) = cos t z(t) = 3 t
, t ∈ [0, 15]
v?&qRKDE=8D3-0524=4/.-Y1*?kJ*U7F74DL;'*E/AkD'D39W24*':/57F/H2F28@'@C-N>EXU7K</.9U24*3B4D?&U^)@3,.,.X'/.9W<DE=8D3-0524=45nI
BFDW*'9m:3DE:?7F/w&R/./.=F=8@W5=4/.,ADE/A7/ADW</.9U2ZD3:?1;/ADW<D3=8DE-05n24=4/.-Y1*?kJ*U7474D0D3995n281728DW</.9JI
9DE728D
x(t) = sin t y(t) = cos t z(t) = u
, t ∈ [0, 2π] , u ∈ [0, 4]
xJ&)yQD324G5-$D324/Az6D+2819U24565j<DE,B*'9W5=4/.,AD3/A7F/ADC{'=4D3|/.::3DE*E,./.*'/H28D0`w}C=8DE<G/.z67~RS=4/.-0/H24/.;E578dZs
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