![]() Practice Problems based on Periodic function If “p” is the period of the periodic function f(x), then af(x) + b, a>0 is also a periodic function with a period of p.The period of Sec (ax + b) and Cosec (ax + b) is 2π/|a|. ![]() The period of Tan (ax + b) and Cot (ax + b) is π/|a|.The period of Sin (ax + b) and Cos (ax + b) is 2π/|a|.If “p” is the period of the periodic function f(x), then f (ax + b), a>0 is also a periodic function with a period of p/|a|.If “p” is the period of the periodic function f (x), then 1/f (x) is also a periodic function and will have the same fundamental period of p as f(x). ![]() ![]() The starting point of the graph of any trigonometric function is taken as x = 0.įor example, if we observe the cosine graph given below, we can see that the distance between two occurrences is 2π, i.e., the period of the cosine function is 2π. In trigonometry, there are three fundamental functions, namely, sin, cos, and tan, whose periods are 2π, 2π, and π periods, respectively. In simple words, it is the distance between the highest or lowest point and the middle point on the graph of a function. Amplitude is defined as the maximum displacement of a particle in a wave from equilibrium. The period of a trigonometric function is the length of one complete cycle. The period of the function is referred to as the distance between the repetitions of any function. sec(x + 2π) = sec x and cosec(x + 2π) = cosec x tan(x + π) = tan x and cot(x + π) = cot x sin(x + 2π) = sin x and cos(x + 2π) = cos x Trigonometric Functions are periodic functions and the period of Trigonometric Functions are as follows The fundamental period of a function is the least value of the positive real number P or the period during which a function repeats itself. A periodic function is one in which there exists a positive real number P such that f (x + p) = f (x), for all x being real numbers. Fundamental period of a functionĪ periodic function’s domain encompasses all real number values while its range is specified for a fixed interval. Below are graphs of some periodic functions, and we can observe that each periodic function’s graph has translational symmetry. Sine wave, triangular wave, square wave, and sawtooth wave are some examples of periodic functions. A periodic function is represented as f(x + p) = f(x), where “p” is the period of the function. In other words, a periodic function is a function whose values recur after a specific time interval.
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