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Mathematics
Mathematics
Problem
2. If
sec
x
d
y
d
x
=
4
tan
y
\sec x \frac{d y}{d x}=4 \tan y
sec
x
d
x
d
y
=
4
tan
y
and
y
(
0
)
=
π
6
y(0)=\frac{\pi}{6}
y
(
0
)
=
6
π
, find an equation for
y
y
y
in terms of
x
x
x
. (A)
sec
2
y
=
3
2
e
4
sin
x
\sec ^{2} y=\frac{\sqrt{3}}{2} e^{4 \sin x}
sec
2
y
=
2
3
e
4
s
i
n
x
(B)
sec
2
y
=
1
2
e
4
sin
x
\sec ^{2} y=\frac{1}{2} e^{4 \sin x}
sec
2
y
=
2
1
e
4
s
i
n
x
(C)
sin
y
=
3
2
e
4
sin
x
\quad \sin y=\frac{\sqrt{3}}{2} e^{4 \sin x}
sin
y
=
2
3
e
4
s
i
n
x
(D)
sin
y
=
1
2
e
4
sin
x
\quad \sin y=\frac{1}{2} e^{4 \sin x}
sin
y
=
2
1
e
4
s
i
n
x
(A)
sec
2
y
=
3
2
e
4
sin
x
\sec ^{2} y=\frac{\sqrt{3}}{2} e^{4 \sin x}
sec
2
y
=
2
3
e
4
s
i
n
x
(B)
sec
2
y
=
1
2
e
4
sin
x
\sec ^{2} y=\frac{1}{2} e^{4 \sin x}
sec
2
y
=
2
1
e
4
s
i
n
x
(C)
sin
y
=
3
2
e
4
sin
x
\quad \sin y=\frac{\sqrt{3}}{2} e^{4 \sin x}
sin
y
=
2
3
e
4
s
i
n
x
(D)
sin
y
=
1
2
e
4
sin
x
\quad \sin y=\frac{1}{2} e^{4 \sin x}
sin
y
=
2
1
e
4
s
i
n
x
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