HOW TO SKETCH THE GRAPH OF SINUSOIDAL FUNCTION

Example :

Sketch the graph of

Solution :

Sketch the graph of y = sin (x).

When x = 0,

y = sin (0)

y = 0

y = 1

When x = π,

y = sin (π)

y = 0

y = -1

When x = 2π,

y = sin (2π)

y = 0

We get the following points from the above table.

Plot the above points on a xy-plane and sketch the graph of y = sin (x).

Comparing

y = a sin [k(x - b)] + N

and

we get

a = 2  and  k = 2

Vertical Stretch/Compression :

a = 2 refers to vertical stretch by a factor of 2.

That is, at each point on the above graph, multiply the y-coordinate by 2.

Horizontal Stretch/Compression :

k = 2 refers to horizontal compression by a factor of 2.

That is, at each point on the above graph, multiply the x-coordinate by ½.

Horizontal Shift :

The above is the graph of the given sinusoidal function. In the given sinusoidal function, since there is no value at the place of N, there is no vertical shift.

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