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Byju's Answer
Standard XIII
Mathematics
Period of Trigonometric Ratios
The period of...
Question
The period of the curve
y
=
sin
4
x
is equal to
A
e
ln
⎷
π
2
4
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B
e
ln
∣
∣
∣
π
4
∣
∣
∣
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C
e
1
2
ln
⎛
⎜
⎝
π
2
16
⎞
⎟
⎠
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D
Period of
y
=
cos
4
x
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Solution
The correct option is
D
Period of
y
=
cos
4
x
Let us draw the graph of
y
=
sin
4
x
We can observe from the graph that the graph is repeated after every interval of length
π
2
.
∴
Period of
sin
4
x
is
π
2
(
i
)
e
ln
⎷
π
2
4
=
π
2
(
i
i
)
e
ln
∣
∣
∣
π
4
∣
∣
∣
=
π
4
(
i
i
i
)
e
1
2
ln
⎛
⎜
⎝
π
2
16
⎞
⎟
⎠
=
π
4
(
i
v
)
Let us draw the graph of
y
=
cos
4
x
We can observe from the graph that the graph is repeated after every interval of length
π
2
.
∴
Period of
cos
4
x
is
π
2
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Period of Trigonometric Ratios
Standard XIII Mathematics
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