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 *x * is looks like this:

Range: [–1, 1] or

*y *-intercept: (0, 1)

*x *-intercept: , where *n * is an integer.

Period:

Continuity: continuous on

Symmetry: origin (odd function)

The maximum value of *y * = sin *x * occurs when , where *n * is an integer.

The minimum value of *y * = sin *x * occurs when , where *n * is an integer.

The amplitude of the graph of *y * = *a * sin *bx * 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 =

**Example :**

Sketch the graphs of *y * = sin *x * and *y * = 2 sin *x *. Compare the graphs.

For the function *y * = 2 sin *x *, the graph has an amplitude 2. Since *b * = 1, the graph has a period of .
Thus, it cycles once from 0 to with one maximum of 2, and one minimum of –2.

Observe the graphs of *y * = sin *x * and *y * = 2 sin *x *. Each has the same *x *-intercepts, but *y * = 2 sin *x * has an amplitude that is twice the amplitude of *y * = sin *x *.

Also see Trigonometric Functions.