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EXAMPLE 5

Find the period of f (t) =

Solution :    If f (t) is periodic with period T then,

where m and n are integers.

Therefore T = 6mp = 8np

When m = 4 and n = 3, we get smallest value of T (by trial and error method)

Hence T = 24p

In general, if the function
f (t) = cos w1t + cos w2t is periodic with
period T then w1T = 2mp and w2T = 2np Þ

i.e. w1 / w2 must be a rational number.

EXAMPLE 6

Is the function f (t) = cos 10 t + cos (10 + p )t periodic ?

Solution :


Therefore we cannot find T. Hence f(t) is not periodic.

EXAMPLE 7

Find the period of the function f(t) = (5 cos t)2

Solution :

We know that cos2x = 1/2 (1 - cos2x)

We have f(t) = (5 cos t)2 = 25 cos2t

Since if f (t) = K, constant function then
f (t+ T) = K = f (t)    \ f (t) is periodic for any T
and cos 2t is periodic with period p.

Index

5. 1 Circular function
5. 2 Periodic function
5. 3 Even & Odd
5.4 Graphs of Trigonometric Functions
Supplementary Problems

Chapter 6

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