2sin3x

The expression "2sin3x" is a mathematical function that combines trigonometric and algebraic elements. It is primarily used in the context of trigonometry and calculus. The function can be broken down into its components: 2 is a constant multiplier, sin represents the sine function, and 3x is the argument of the sine function, where x is the variable.

The sine function, sin(x), is a periodic function with a period of 2π. This means that sin(x) repeats its values every 2π units along the x-axis. When the argument of the sine function is multiplied by a constant, such as in 2sin3x, the period of the function changes. Specifically, the period of 2sin3x is given by 2π/3, which is approximately 2.094 radians or about 120 degrees.

The amplitude of the function 2sin3x is 2, which is the coefficient of the sine function. This means that the maximum and minimum values of the function are 2 and -2, respectively.

The function 2sin3x is differentiable, meaning it has a derivative at every point. The derivative of 2sin3x with respect to x is 6cos3x. This derivative represents the rate of change of the function at any given point.

In summary, 2sin3x is a trigonometric function with a period of 2π/3 and an amplitude of 2. It is used in various mathematical and scientific applications, particularly in the study of periodic phenomena.