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Byju's Answer
Standard X
Mathematics
Range of Trigonometric Ratios from 0 to 90 Degrees
The period of...
Question
The period of the function
f
(
x
)
=
cos
(
8
x
+
5
4
π
)
is
A
π
2
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B
π
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C
π
2
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D
none of these
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Solution
The correct option is
A
π
2
∵
Period of
cos
x
is
2
π
.
∴
Period of
f
(
x
)
=
cos
(
8
x
+
5
4
π
)
is
=
2
π
8
4
π
⇒
π
2
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0
Similar questions
Q.
The period of the function
f
(
x
)
=
cos
(
8
x
+
5
4
π
)
Q.
Find
α
and
β
, so that the function
f
(
x
)
defined by
f
(
x
)
=
−
2
sin
x
,
for
−
π
≤
x
≤
−
π
2
=
α
sin
x
+
β
,
for
−
π
2
<
x
<
π
2
=
cos
x
,
for
π
2
≤
x
≤
π
is continuous on
[
−
π
,
π
]
.
Q.
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
(a) increasing
(b) decreasing
(c) constant
(d) none of these
Q.
Assertion :Consider
f
(
x
)
=
lim
n
→
∞
{
x
1
+
{
3
tan
2
x
}
n
}
f
(
x
)
is periodic function with period
π
. Reason:
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
0
,
−
π
2
<
x
<
−
π
6
x
2
,
x
=
−
π
6
x
,
−
π
6
<
x
<
π
6
x
2
,
x
=
π
6
0
,
π
6
<
x
<
π
2
Q.
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
−
2
sin
x
,
−
π
≤
x
≤
−
π
2
a
cos
(
x
)
+
b
,
−
π
2
<
x
<
0
−
2
+
cos
x
,
0
≤
x
≤
π
2
c
sin
x
,
π
2
<
x
≤
π
⎫
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎭
is continuous in
[
−
π
,
π
]
,
then number of points at which
f
(
x
)
is not differentiable is/are
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