Sine of reciprocal function

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This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
View a complete list of particular functions on this wiki
For functions involving angles (trigonometric functions, inverse trigonometric functions, etc.) we follow the convention that all angles are measured in radians. Thus, for instance, the angle of 90\,^\circ is measured as \pi/2.

Definition

This function is defined as the composite of the sine function and the reciprocal function. In other words, it is the function:

x \mapsto \sin(1/x), \qquad x \ne 0

Graph

Here is the graph, at various levels of magnification:

Sin1byx.png

Sin1byx-1to1.png

Sin1byxzoomin1.png

Sin1byxzoomin2.png