find general solution of: 2Cos3X-1=0
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Answers
Answered by
2
The period of the
cos
(
3
x
)
cos(3x) function is
2
π
3
2π3 so values will repeat every
2
π
3
2π3 radians in both directions.
x
=
π
9
+
2
π
n
3
,
5
π
9
+
2
π
n
3
x=π9+2πn3,5π9+2πn3, for any integer
n
n
Answered by
0
Step-by-step explanation:
Values that
x
can take in interval are
[
0
,
2
π
]
are
{
π
9
,
5
π
9
,
7
π
9
,
11
π
9
,
13
π
9
,
17
π
9
}
Explanation:
As
2
cos
3
x
=
1
, we have
cos
3
x
=
1
2
=
cos
(
π
3
)
Hence
3
x
=
2
n
π
±
π
3
, where
n
is an integer.
Hence,
3
x
can take values
{
...
...
,
−
5
π
3
,
−
π
3
,
π
3
,
5
π
3
,
7
π
3
,
11
π
3
,
13
π
3
,
17
π
3
,
19
π
3
,
...
.
}
and
x
can take values
{
...
...
.
,
−
5
π
9
,
−
π
9
,
π
9
,
5
π
9
,
7
π
9
,
11
π
9
,
13
π
9
,
17
π
9
,
19
π
9
,
...
.
}
and values that
x
can take in interval are
[
0
,
2
π
]
are
{
π
9
,
5
π
9
,
7
π
9
,
11
π
9
,
13
π
9
,
17
π
9
}
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