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Byju's Answer
Standard XII
Mathematics
Bijective Function
For what valu...
Question
For what values of
x
∈
(
2
π
,
8
π
)
,
sin
x
≤
0
?
A
x
∈
[
3
π
,
4
π
]
∪
[
5
π
,
6
π
]
∪
[
7
π
,
8
π
]
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B
x
∈
(
3
π
,
4
π
]
∪
[
5
π
,
6
π
]
∪
[
7
π
,
8
π
)
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C
x
∈
[
3
π
,
4
π
]
∪
[
5
π
,
6
π
]
∪
[
7
π
,
8
π
)
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D
x
∈
(
3
π
,
4
π
]
∪
[
5
π
,
6
π
]
∪
[
7
π
,
8
π
]
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Solution
The correct option is
C
x
∈
[
3
π
,
4
π
]
∪
[
5
π
,
6
π
]
∪
[
7
π
,
8
π
)
Given, the graph of
y
=
sin
x
:
sin
x
≤
0
⇒
The graph of
sin
x
should lie below the
x
−
axis in the particular interval.
Now, for
x
∈
(
2
π
,
8
π
)
highlighting the region where
sin
x
≤
0
:
From the graph, we can see the values of
x
for which
sin
x
≤
0
is
x
∈
[
3
π
,
4
π
]
∪
[
5
π
,
6
π
]
∪
[
7
π
,
8
π
)
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