periodic functions and their properties
(i) Graph of periodic function with period T is repeated after every interval of T
Lenth of interval(2,5)=Higher level - lower level
=5-2
=3
Lenth of interval(0,2π)=Higher level - lower level
=2π - 0
=2π
[0,π] period = π
(ii) sinx ,cosx,secx and cosecx are periodic functions with period 2π.
(iii) tanx and cotx are periodic function with π.
(iv) |sinx| , |cosx| , |tanx|, |cotx|, |secx| and |cosecx| are periodic function with period π.
(v) sin^n x , cos^n x, sec^n x and csc^n x are periodic function with period π or 2π according as n in even or odd.
(vi) tan^n x and cot^n x are periodic functions with period π when n is even or odd.
e.g period of sin^4 x = π
cos^53 x = 2π
tan^20 x = π
tan^101 x = π
(vii) {x} ,where {.} denotes F.P.E is periodic function with period 1.
(viii) Algebric functions are not periodic.
(ix) constant function is periodic function with no fundamental period.
(x) Inverse of periodic function does not exist.
(xi) Every contineous periodic function is bounded.
(xii)If f(x) is periodic Function with period T ,then
(a) cf(x) ,where c≠0 , is also a periodic function with period T.
(b)f(x) ± c is also a periodic function with period T.
(c)√f(x) is also a periodic Function with period T.
(d) 1/f(x) is also a periodic function with period T.
e.g period of 3sinx = 2π
cos^4x +7 =π
sin^2x → π
√sin^2x → π
list of periodic functions
periodic function pdf
application of periodic function
periodic function definition
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periodic function examples in real life
