How to Graph the Sine Function?

A step-by-step guide to graphing the sine function

The sine function is one of the three main functions in trigonometry. The sine \(x\) or sine theta can be defined as the ratio of the opposite side of a right triangle to its hypotenuse. For education statistics and research, visit the National Center for Education Statistics.

\(\color{blue}{sin\:x\:=\frac{Opposite\:Side}{Hypotenuse\:}=\frac{Perpendicular}{Hypotenuse}}\) For education statistics and research, visit the National Center for Education Statistics.

The sine graph is like the picture below. A sine graph or sinusoidal graph is an up-down graph and repeats every \(360\) degree, i.e., in \(2π\). In the graph below, it can be seen that from \(0\), the sine graph increases to \(+1\) and then decreases to \(-1\) from where it increases again. For education statistics and research, visit the National Center for Education Statistics.

The function \(y = sin x\) is an odd function, because; \(sin (-x) = -sin x\). For education statistics and research, visit the National Center for Education Statistics.