sin2cos2

Sin2cos2 refers to the product sin(2) cos(2), i.e., the sine and cosine of the same angle measured in a given unit. A standard trigonometric identity says that sin x cos x = (1/2) sin(2x). Applying this with x = 2 gives sin 2 cos 2 = (1/2) sin 4. The value depends on the angular unit: if the numbers are in radians, sin 4 ≈ -0.7568, so sin 2 cos 2 ≈ -0.3784. If the numbers are in degrees, sin 4° ≈ 0.06976, and sin 2° cos 2° ≈ 0.03488, which equals (1/2) sin 4°.

General properties include that sin x cos x is bounded between -1/2 and 1/2, since |sin x cos x| ≤ 1/2 with equality when x = π/4 + kπ. The identity sin x cos x = (1/2) sin 2x also shows the expression is a rescaled sine wave as x varies, with period π in radians (or 180° in degrees).

Related topics include product-to-sum formulas, which convert products of sine and cosine into sums of sines, and their use in simplifying trigonometric expressions, Fourier analysis, and signal processing. The specific case sin 2 cos 2 is a simple illustration of how a product can be rewritten as a single sine function of a doubled angle, revealing both algebraic relationships and numeric evaluations.