4cosx

4cosx refers to the mathematical function obtained by multiplying the cosine function, cos(x), by the constant value of 4. The cosine function, 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 length of the hypotenuse. In the context of the unit circle, cos(x) represents the x-coordinate of a point on the circle corresponding to an angle x measured counterclockwise from the positive x-axis.

When the cosine function is multiplied by 4, the resulting function, 4cosx, undergoes a vertical stretch. This means that the amplitude of the function is increased. The standard cosine function has an amplitude of 1, meaning its values oscillate between -1 and 1. For 4cosx, the values will oscillate between -4 and 4. The period of the function remains unchanged, which is 2π. This means that the function completes one full cycle over an interval of 2π radians. The graph of 4cosx will appear as a stretched version of the graph of cosx, with its peaks and troughs extended further from the x-axis. This transformation is often encountered in various fields, including physics (e.g., in describing simple harmonic motion with a different amplitude) and engineering.