Graphing Sine Function

The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given in degrees or radians . Here, we will use radians.

The graph of a sine function $y=\sin \left(x\right)$ is looks like this:

Properties of the Sine Function, $y=\sin \left(x\right)$

Domain : $(-\infty ,\infty )$

Range : $\left[-1,1\right]$ or $-1\le y\le 1$

$y$ -intercept : $(0,0)$

$x$ -intercept : $n\pi$ , where $n$ is an integer.

Period: $2\pi$

Continuity: continuous on $(-\infty ,\infty )$

Symmetry: origin (odd function)

The maximum value of $y=\sin \left(x\right)$ occurs when $x=\frac{\pi }{2}+2n\pi$ , where $n$ is an integer.

The minimum value of $y=\sin \left(x\right)$ occurs when $x=\frac{3\pi }{2}+2n\pi$ , where $n$ is an integer.

Amplitude and Period of a Since Function

The amplitude of the graph of $y=a\sin \left(bx\right)$ is the amount by which it varies above and below the $x$ -axis.

Amplitude = | $a$ |

The period of a sine function is the length of the shortest interval on the $x$ -axis over which the graph repeats.

Period = $\frac{2\pi }{\left|b\right|}$

Also see Trigonometric Functions .