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Mathematics
Mathematics
Problem
For a particle, the velocity components are
d
x
d
t
=
cos
(
t
+
π
4
)
\dfrac{dx}{dt}=\cos\bigl(t+\tfrac{\pi}{4}\bigr)
d
t
d
x
=
cos
(
t
+
4
π
)
and
d
y
d
t
=
sin
(
t
+
π
4
)
\dfrac{dy}{dt}=\sin\bigl(t+\tfrac{\pi}{4}\bigr)
d
t
d
y
=
sin
(
t
+
4
π
)
. At time
t
=
−
π
4
t=-\tfrac{\pi}{4}
t
=
−
4
π
the particle is located at
(
2
,
0
)
(2,0)
(
2
,
0
)
. Determine the parametric equations
x
(
t
)
x(t)
x
(
t
)
and
y
(
t
)
y(t)
y
(
t
)
valid for all real
t
t
t
.
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