sinxsinx

The function sinxsinx, more commonly written as sin^2(x) or (sin x)^2, is a trigonometric function that represents the square of the sine of an angle x. It is a fundamental component in calculus and various areas of physics and engineering. The value of sin^2(x) always ranges between 0 and 1, inclusive, as the sine function itself oscillates between -1 and 1. When the sine of an angle is 0, its square is also 0. When the sine of an angle is 1 or -1, its square is 1.

The graph of sin^2(x) is a periodic wave, similar to the sine wave but with all its values non-negative. It completes a full cycle over an interval of pi radians, half the period of sin(x). This property makes it useful in analyzing phenomena that exhibit oscillations with squared amplitudes, such as intensity in wave mechanics or power in electrical circuits.

Sin^2(x) is closely related to the cosine function through the Pythagorean identity sin^2(x) + cos^2(x) = 1. This identity allows for its direct substitution or manipulation in trigonometric identities and equations. Integration of sin^2(x) is a common calculus problem, often solved by using the power-reduction formula, which expresses sin^2(x) in terms of cos(2x).