Page 35 - Mathematics Class - XI

DEMONSTRATION
x
Plot the ordered pair (x, sin x), (x, sin 2x), (x, 2 sin x) and (x, sin 2 ) on the same axes of coordinates, and join

them by free hand curves, by using different colour pencils for each as shown in Fig. (b).

Angles (in degree)

Fig. (b)

OBSERVATION

1. Graph of sin x and 2 sin x are of same shape but the maximum height of the graph of 2 sin x is double the
maximum height of the graph of sin x.
p
2. The maximum height of the graph of 2 sin x is 2 units. It is at x = .
2

p
3. The maximum height of the graph of sin 2x is 1 unit. It is at x = .
4
x
4. The maximum height of the graph of sin is 1 unit. It is at x = p.
2
x
5. At x = 0, sin x = 0, sin 2x = 0, sin = 0.
2
x
6. In the interval (0, p), graphs of sin x, 2 sin x and sin are above the x-axis and some portion of the graph
of sin 2x lies below x-axis. 2
p
7. Graphs of sin x and sin 2x intersect at x = in the interval (0, p).
3
x 2p
8. Graphs of sin x and sin intersect at x = in the interval (0, p).
2 3

CONCLUSION
This activity explores the different sine curves using the same coordinate axes.

APPLICATION
This activity can be used in tracing of trigonometric curves and can be applied in the field of physics.

Knowledge Booster
The amplitude of the function is defined as the greatest numerical value which it can attain.
It is always a positive quantity.

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