Page 26 - Mathematics Class - XII

ACTIVITY 2.2

OBJECTIVE
To explore the principal value of the function sin x, using a unit circle.
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MATERIAL REQUIRED
Y Cardboard Y Two steel rods
Y White sheet Y Adhesive

Y Pen or sketch pens Y Geometry box
Y Paper pins / thumb pins

PRE-REQUISITE KNOWLEDGE
1. Knowledge of inverse trigonometric functions.
2. Knowledge of periodic functions.
3. Knowledge of principal value branch.

PROCEDURE
1. Take a cardboard of dimension 30 cm × 30 cm.

2. Paste a white sheet on cardboard with thumb pins or glue as shown in Fig. (a).
3. Draw two perpendicular lines XOX′ and YOY′ representing X-axis and Y-axis respectively with O being
the origin as shown in Fig. (b).

Y
B (0, 1)
Needle

(–1, 0) C A (1, 0)
X′ O X

D (0, –1)
Y′
Fig. (a) Fig. (b)

4. By taking O as centre, draw a circle of radius = 1 unit, as shown in Fig. (b). Mark the points A (1, 0), C (–1, 0),
B (0, 1) and D (0, –1), where the circle cuts the x-axis and y-axis, respectively as shown in Fig. (b).

5. Fix a rotating needle of unit length with one fixed end at the centre ‘O’.
6. Fix two rod parallel to y-axis on the opposite sides of the cardboard as shown in Fig. (c) given below.

7. Now fix one steel wire between the rods so that the wire can be moved freely parallel to x-axis as shown
in Fig. (c) given below.

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