Match the equations with the graphs labeled I–IV and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant. 14. x = ( 1 − u ) ( 3 + cos v ) cos 4 π u , y = ( 1 − u ) ( 3 + cos v ) sin 4 π u , z = 3 u + ( 1 − u ) sin v
Match the equations with the graphs labeled I–IV and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant. 14. x = ( 1 − u ) ( 3 + cos v ) cos 4 π u , y = ( 1 − u ) ( 3 + cos v ) sin 4 π u , z = 3 u + ( 1 − u ) sin v
Solution Summary: The author compares the parametric equations with the graphs labeled I-VI in the book to explain the reason for the combination.
Match the equations with the graphs labeled I–IV and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant.
14.
x
=
(
1
−
u
)
(
3
+
cos
v
)
cos
4
π
u
,
y
=
(
1
−
u
)
(
3
+
cos
v
)
sin
4
π
u
,
z
=
3
u
+
(
1
−
u
)
sin
v
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