sin1x

sin1x is typically read as the sine of the product 1 and x, i.e., sin(1x). Because 1x equals x, sin1x is simply sin(x) in standard mathematical notation. In other words, the expression does not change the input to the sine function; it is an equivalent way of writing sin x.

Notation caveat: sin−1 x refers to the inverse sine function, arcsin x, not to sin(1x). Therefore, sin1x should not be interpreted as arcsin x. In practice, sin(1x) and sin x denote the same function, while sin−1 x denotes a different function altogether.

Domain and range: As a function of a real variable x, sin1x = sin x has domain all real numbers and range from −1 to 1. The sine function is periodic with period 2π and is an odd function, meaning sin(−x) = −sin(x).

Angle units: In pure mathematics, angles are usually measured in radians; sin(1x) assumes radians unless otherwise stated. If x is given in degrees, the input must be converted to radians for calculation, since the sine function’s standard form uses radians. The numerical period changes accordingly when degrees are used.

Derivative and simple values: By the chain rule, d/dx sin(1x) = cos(1x)·d/dx(1x) = cos(x). Simple evaluations follow common sine values, e.g., sin(1·π/6) = sin(π/6) = 1/2.

Summary: sin1x is a redundant notation for sin(x) in standard contexts, retaining the same properties and values as the ordinary sine function.