sinNsin2

SinNsin2 denotes the product sin(N) sin(2), where N is typically an integer or real variable and the arguments are in radians unless otherwise stated. It is a simple trigonometric expression that combines two sine functions: one with argument N and one with the fixed argument 2.

A useful identity for this expression is the product-to-sum formula: sin N sin 2 = 1/2 [cos(N − 2) − cos(N + 2)]. This transformation converts the product into a difference of cosines, which can simplify certain analyses, such as summations or Fourier-type manipulations.

Properties of the value depend on N. Since |sin(N)| ≤ 1 and sin(2) is a constant (approximately sin(2) ≈ 0.9093), the magnitude satisfies |sin(N) sin(2)| ≤ |sin(2)| ≈ 0.9093. The sign varies with N. If N is restricted to integers, the sequence {sin(N) sin(2)} is dense in the interval [−sin(2), sin(2)], due to the fact that the values N mod 2π are dense in [0, 2π).

Notes and variants. The expression is typically interpreted as the product sin(N)·sin(2). If the intended form were sin(N sin 2) or sin(N) sin^2(2), those would be different functions. The standard reading remains a simple product, often used in problems involving trigonometric sums, transformations, or as a unit example of how product-to-sum identities operate with a fixed versus a variable argument.