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| Graph of y = sin x |
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| Now let us construct the graph of y = sinx from x = 0o to 360o. The following table is readily constructed for intervals of 30o. |
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| Plotting the points and drawing a smooth curve through them we have the curve as shown in figure. |
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| From the figure it is evident that the curve repeats itself every 360o or 2p. This fact is expressed by saying that the function has a period of 360o or 2p. |
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| In symbols we write sin (x + n.360o) or sin (x + 2np), sinx = sin (x + n.360o) = 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 0o to 90o, sinx increases from 0 to 1 and as x increases from 90o to 180o, sinx decreases from 1 to 0. |
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| [A function f(x) is periodic with period T if f(x+T) = f(x) for all values of x] |
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| As x increases from 180o to 270o, sinx decreases from 0 to -1 and as x increases from 270o to 360o, sinx increases from -1 to 0. The maximum absolute value of sin x = 1. |
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