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Mathematics
Mathematics
Problem
An angle
θ
(
t
)
\theta(t)
θ
(
t
)
(in radians) satisfies
tan
θ
(
t
)
=
0.5
t
\tan \theta(t)=0.5t
tan
θ
(
t
)
=
0.5
t
for
t
≥
0
t\ge 0
t
≥
0
. Define the function
k
(
t
)
=
sin
(
θ
(
t
)
2
)
k(t)=\sin\!\bigl(\theta(t)^{2}\bigr)
k
(
t
)
=
sin
(
θ
(
t
)
2
)
. Determine
d
k
d
t
\dfrac{dk}{dt}
d
t
d
k
at
t
=
1
t=1
t
=
1
.
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