Points observed from the graph

1) The graph of sinx and cosx have no breaks and they lie between y=1 and y = -1. So sinx and cosx are continuous for all values of x and the values of sinx and cosx always lie between 1 and +1. Hence sinx and cosx are bounded function.

2) There are breaks in the graph of tanx.

At these points tan q is not defined and tanx is a discontinuous function. The graph of tanx is not bounded and can assume all real values.

Graph of y=a sin bx and y=a cos bx

If we compare the graph of y=a sin bx with y=sin x we observe that sin bx has values between +1 and -1 (both values inclusive) on the values of sinx.

Example:

Sketch the graphs of the following:

(i) y = sin 3x and y = 2 sin 3x

(ii) y = tan 2x

(i) y = sin 3x and y = 2 sin 3x

Table:

Graph:

(ii) tan 2x

Table:

Graph: