MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
2017 AMC 12/AHSME
15
15
Part of
2017 AMC 12/AHSME
Problems
(1)
T R I G g e r e d
Source: AMC 12 2017A/15
2/8/2017
Let
f
(
x
)
=
sin
x
+
2
cos
x
+
3
tan
x
f(x)=\sin x+2\cos x+3\tan x
f
(
x
)
=
sin
x
+
2
cos
x
+
3
tan
x
, using radian measure for the variable
x
x
x
. In what interval does the smallest positive value of
x
x
x
for which
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
lie?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
(
0
,
1
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
(
1
,
2
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
(
2
,
3
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
(
3
,
4
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
(
4
,
5
)
<span class='latex-bold'>(A) </span> (0,1) \qquad <span class='latex-bold'>(B) </span> (1,2) \qquad <span class='latex-bold'>(C) </span> (2,3) \qquad <span class='latex-bold'>(D) </span> (3,4) \qquad <span class='latex-bold'>(E) </span> (4,5)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
(
0
,
1
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
(
1
,
2
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
(
2
,
3
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
(
3
,
4
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
(
4
,
5
)
AMC
AMC 12
2017 AMC 12A