sinpi2

Sinpi2 is a notation that you may encounter in mathematics and programming referring to the sine of pi over two, written as sin(π/2). In exact mathematics, sin(π/2) equals 1. On the unit circle, the angle π/2 corresponds to the point (0, 1), which reflects that the sine value is the y-coordinate.

As a consequence, sin(π/2) = 1, cos(π/2) = 0, and tan(π/2) is undefined due to division by zero. The sine function is periodic with period 2π, so sin(π/2 + 2πk) = 1 for any integer k. Related identities include sin(π/2 + x) = cos x and sin(π/2 − x) = cos x.

In numerical computation, sin(π/2) is typically evaluated to be extremely close to 1, with small floating-point errors depending on the implementation. In degrees, sin(90°) also equals 1, highlighting the connection between radian and degree measures.

Notes on notation: sinpi2 is not a universally standardized mathematical symbol. In some programming libraries, sinpi denotes a function that computes sin(πx), and the form sinpi2 may be used informally to indicate evaluation at a particular argument, with the exact meaning depending on context. Therefore, the precise interpretation of sinpi2 should be inferred from the surrounding notation. See also sine, unit circle, and trigonometric identities.