Graph of y = sin x

Now let us construct the graph of y = sinx from x = 0^o to 360^o. The following table is readily constructed for intervals of 30^o.

Plotting the points and drawing a smooth curve through them we have the curve as shown in figure.

Table:

Graph:

From the figure it is evident that the curve repeats itself every 360^o or 2p. This fact is expressed by saying that the function has a period of 360^o or 2p.

In symbols we write sin (x + n.360^o) or sin (x + 2np), sinx = sin (x + n.360^o) = sin (x + 2np), where n is any positive or negative integer. This infers that sinx varies and takes a complete ordered range of values once and that sinx is periodic has the period 2p. From the figure we observe that as x increases from 0^o to 90^o, sinx increases from 0 to 1 and as x increases from 90^o to 180^o, sinx decreases from 1 to 0.

[A function f(x) is periodic with period T if f(x+T) = f(x) for all values of x]

As x increases from 180^o to 270^o, sinx decreases from 0 to -1 and as x increases from 270^o to 360^o, sinx increases from -1 to 0. The maximum absolute value of sin x = 1.