CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Which of the following functions has a period of 2π ?

A
f(x)=sin(2πx+π3)+2sin(3πx+π4)+3sin5πx
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
f(x)=sinπx3+sinπx4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
f(x)=sinx+cos2x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B f(x)=sinx+cos2x
Option A, f(x)=sin(2πx+π3)+2sin(3πx+π4)+3sin5πx
Period of sin(2πx+π3) is 2π2π=1
Period of 2sin(3πx+π4)is 2π3π=23
Period of 3sin5x is 2π5π=25
LCM of 1,23,25=LCMof1,2,2HCFof3,5=2
So, period of f(x) is 2.
B) f(x)=sinπx3+sinπx4

Period of sinπx3 is 2ππx3=6
Period of sinπx4 is 2ππx4=8
LCM of 6 and 8 is 24.

So, period of f(x) is 24.
C) f(x)=sinx+cos2x
Period of sinx is 2π
Period of cos2x is 2π2=π
LCM of 2π,π is 2π
Hence, period of f(x) is 2π

Period of f(x)=sinx+cos2x=2π

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parametric Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon