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EXAMPLE 1

Find the fundamental period of f (t) = sin kt1 For k > 0

Solution : We know that,

\ f (t) is periodic function with fundamental period

EXAMPLE 2

Find whether f (t) = cos (5t + 4) is periodic? If so, find its fundamental period.

Solution :    Since cos t = cos (t + 2p)

\ f (t) is a periodic function and the fundamental period is 2p/5.

EXAMPLE 3

Find a tangent function whose fundamental period is 9.

Solution:     tan t = tan (t + p)

Let f (t) = tan kt be the required function

\ f (t) = tan kt = tan (kt + p)

EXAMPLE 4

If sin x = 3/5 then what is the value of each of the following sin (x + 6p), sin (x + 36000), sin(x -10800).

Solution:     sin (x + 6p) = sin (x + 2p),

sin (x + 36000) = sin (x + 10p) = sin (x + 2p) and

sin (x - 10800) = sin (x - 6p) = sin (x - 2p)

\ sin (x + 6p) = sin (x + 2p) = sin (x - 2p) = 3/5 since the function is periodic with period 2p.

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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