Which of the following functions are periodic Provide justif

Which of the following functions are periodic? Provide justification for your answers. State the period of those functions that are periodic.
(A) y=sin(-t)
(B) y=cos(pi(t))
(C) y=sin (t)+1
(D) y=sin(t/2)+1

Solution

A periodic function is one that repeats itself in regular intervals. These intervals are called periods of the function. It is the minimum interval within which the function has distinct values, its graph shows different slopes all along and different curvatures for its curve.

Given by, f(x) = f(x+T) = f(x+2T) = f(x+3T) = …. where T is period of function f(x).

Use the form a*sin(bx - c) + d

Period = 2pi/b

(A) y = sin(-t) ======>Periodic

Period = 2pi

(B) y = cos(pi(t)) ======>Periodic

Period = 2

(C) y = sin (t) + 1======>Periodic

Period = 2pi

(D) y = sin(t/2) + 1======>Periodic

Period = 4pi