MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
2021 AMC 12/AHSME Fall
19
19
Part of
2021 AMC 12/AHSME Fall
Problems
(1)
Sine Goes Bonkers
Source: 2021 AMC 12A (Fall) #19
11/11/2021
Let
x
x
x
be the least real number greater than
1
1
1
such that
sin
(
x
)
\sin(x)
sin
(
x
)
=
sin
(
x
2
)
\sin(x^2)
sin
(
x
2
)
, where the arguments are in degrees. What is
x
x
x
rounded up to the closest integer?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
10
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
13
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
14
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
19
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
20
<span class='latex-bold'>(A) </span> 10 \qquad <span class='latex-bold'>(B) </span> 13 \qquad <span class='latex-bold'>(C) </span> 14 \qquad <span class='latex-bold'>(D) </span> 19 \qquad <span class='latex-bold'>(E) </span> 20
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
10
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
13
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
14
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
19
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
20
trigonometry