Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
x
(
t
)
=
2
2
(
cos
t
)
sin
2
t
x(t) = 2\sqrt{2}(\cos t)\sqrt{\sin 2t}
x
(
t
)
=
2
2
(
cos
t
)
sin
2
t
and
y
(
t
)
=
2
2
(
sin
t
)
sin
2
t
y(t) = 2\sqrt{2}(\sin t)\sqrt{\sin 2t}
y
(
t
)
=
2
2
(
sin
t
)
sin
2
t
,
t
∈
(
0
,
π
2
)
t \in (0, \frac{\pi}{2})
t
∈
(
0
,
2
π
)
. Then
1
+
(
d
y
d
x
)
2
d
y
d
x
at
t
=
π
4
is equal to
\frac{1 + \left(\frac{dy}{dx}\right)^2}{\frac{dy}{dx}} \text{ at } t = \frac{\pi}{4} \text{ is equal to}
d
x
d
y
1
+
(
d
x
d
y
)
2
at
t
=
4
π
is equal to
Browse the problem library