The argument of the cosine function must be (2pi/3)*x radians
A function f(x) of the variable x, has a period k where k is some constant, if f(x+ k) = f(x) for every x. It is easy to show that f(x + nk) = f(x) for any integer n. What the above two formulae imply is that the values of the function repeat after an interval (or period) of k. The trigonometric functions are some of the better known periodic functions.
The period of the tangent function is PI. The period of y= tan(2x) is PI over the coefficient of x = PI/2
No. It is an increasing function, with a domain of x > 0. An example of a periodic function is y = sin x. It repeats with every period and keeps crossing, back and forth, over the x-axis. y = log x doesn't behave that way. It just keeps increasing, without limit, as x increases.
The first part of the question is false, and the correct answer is that an even function of minus x equals the function positive x. This follows from the very definition of an even function. The second part of the question is false, because the truth is that the composite function results from taking the function of x within the function g.
A nonconstant function is called periodic if there exists a number that you can add to (or subtract from) the argument and get the same result. The smallest such positive number is called the period. That is, nonconstant function f(x) is periodic, if and only if f(x) = f(x + h) for some real h. The smallest positive such h is the period. For example, the sine function has period 2*pi, and the function g(x) := [x] - x has period 1.
You can invent any function, to make it periodic. Commonly used functions that are periodic include all the trigonometric functions such as sin and cos (period 2 x pi), tan (period pi). Also, when you work with complex numbers, the exponential function (period 2 x pi x i).
The period of trigonometric function is the distance between repetitions of the function. The "x" value of the space it takes to start over.
y = 3 sin x The period of this function is 2 pi.
The period of the function y= tan(x) is pie The periods of the functions y= cos(x) and y= sin(x) is 2pie
The period of the function y= tan(x) is pie The periods of the functions y= cos(x) and y= sin(x) is 2pie
There are an infinite number. The simplest is a sinusoid. The sine function has period 2π, so you compress it by a factor of π: f(x) = sin (πx).
A function f(x) has period t if t is the smallest value such thatf(x+t) = f(x) for all x in the appropriate domain.
It is the same period as cosine function which is 2 pi because sec x = 1/cos x
2 pi
The argument of the cosine function must be (2pi/3)*x radians
It is pi/5 radians.