2sin2x

The expression 2sin2x is a trigonometric function that can be derived from the double-angle identity for sine. The double-angle identity for sine states that sin(2x) = 2sin(x)cos(x). By multiplying both sides of this identity by 2, we obtain the expression 2sin2x = 4sin(x)cos(x). This expression is useful in various mathematical and scientific applications, including physics, engineering, and signal processing.

The graph of the function y = 2sin2x is a sine wave with an amplitude of 2 and a period of π. The amplitude of a sine wave is the maximum distance from the centerline to the peak or trough, and the period is the distance between two consecutive peaks or troughs. In the case of y = 2sin2x, the amplitude is 2, which means that the maximum value of the function is 2 and the minimum value is -2. The period is π, which means that the function completes one full cycle as x increases from 0 to π.

The expression 2sin2x can also be used to derive other trigonometric identities. For example, by squaring both sides of the identity 2sin2x = 4sin(x)cos(x), we obtain the identity sin^2(2x) = 4sin^2(x)cos^2(x). This identity can be used to simplify expressions involving trigonometric functions and to solve problems in various fields of mathematics and science.