3cosx

3cosx refers to the mathematical function of three times the cosine of x. The cosine function, denoted as cos(x), is a fundamental trigonometric function that relates an angle of a right-angled triangle to the ratio of the length of the adjacent side to the hypotenuse. In the context of the unit circle, cos(x) represents the x-coordinate of a point on the circle at an angle x radians from the positive x-axis.

The function 3cosx is a vertical stretch of the basic cosine graph by a factor of 3. This means that the amplitude of the wave is increased. The standard cosine function has an amplitude of 1, meaning its values oscillate between -1 and 1. For 3cosx, the values will oscillate between -3 and 3. The period of the function remains the same as the basic cosine function, which is 2π radians (or 360 degrees). This means that the graph of 3cosx repeats its pattern every 2π interval.

The domain of 3cosx is all real numbers, as the cosine function is defined for any angle. The range of 3cosx is the closed interval [-3, 3]. This function is an even function, meaning that cos(-x) = cos(x), and therefore 3cos(-x) = 3cosx. Graphs of 3cosx are smooth, continuous waves that are symmetric about the y-axis. It is frequently used in various fields, including physics, engineering, and signal processing, to model periodic phenomena.