Mathematics Lab Activity-7 Class XI

Mathematics Laboratory Activities on Trigonometric Functions for class XI students Non-Medical. These activities are strictly according to the CBSE syllabus

Chapter - 3 | trigonometric functions

Activity - 7

Objective

To verify the relation between the degree measure and the radian measure of an angle.

Material Required

Geometry  box, protractor, thread, marker, cardboard, white paper. 

Theory

Angle : An angle is a measure of rotation of a given ray about its initial point. The angle is said to be positive if the direction of rotation is anticlockwise and the angle is said to be negative if the direction of rotation is clockwise.

Units used for measuring angles

(i) Degree Measure : If the rotation from the initial side to the terminal side is  (1/360)^th  of a revolution, then the angle is said to have a measure of one degree, written as 1^o 

1^o = 60’ (Minutes)

1’ = 60’’ (Seconds)

(ii) Radian Measure:

One radian is defined as the angle subtended at the centre of a circle by an arc whose length is equal to its radius.

Relation between radian and degree

2π radian = 360^o

π radian = 180^o

Note: The angle subtended at the centre of a circle, of radius r, by an arc of length l is given by  θ = l/r (In radian)

Procedure

 1. Paste a white or yellow  paper on a card board of convenient size.

2. Draw two  circles on the white or yellow  paper with the help of compass.

3. Draw two  diameters AB and CD on the first circle as shown in the fig. 7.1 .

4. Both diameters AB and CD of the circle intersect at the point O.  Therefore : OA = OB = OC = OD = are the radius of the circle = r(say)

5. In figure 7.2 Take an arc PQ of the circle. Let its length be l. Join OP and OQ . Let θ be the angle subtended by this arc at the centre of the circle.

6. Length of arc is given by   

⇒ 1 Radian = 57^o16’21’’ = (57.27)^o

7. In figure 7.1 measure the lengths of arcs AC, AD, BD and BC with the help of a thread and a metre - scale  measure the radius OA = OB = OC = OD and measure the angles in degree with the help of protractor.

Observations

Table 1

S. No.	Arc	Length of arc(l)	Radius of circle(r)	Angle in radian measure
1	AC	11 cm	14 cm
2	AD	33 cm	14 cm
3	BD	11 cm	14 cm
4	BC	33 cm	14 cm

Table 2:

Angle	Degree Measure	Radian Measure
∠AOC	45o	π/4	180/π = 57o16’21’’ = 57.27o
∠AOD	135o	3π/4	180/π = 57o16’21’’ = 57.27o
∠BOD	45o	π/4	180/π = 57o16’21’’ = 57.27o
∠BOC	135o	3π/4	180/π = 57o16’21’’ = 57.27o

The value of one radian is = 57.27^o

Result

1 Radian = 57^o16’21’’ = 57.27^o

Applications

This result is very useful in the study of trigonometric functions.

VIVA – VOICE

Q. 1. What do you mean by an angle ?

Ans. An angle is the measure of rotation of a given ray about its initial point.

Q. 2. When is the angle said to be positive.

Ans. If the direction of rotation of the given angle is anticlockwise , then the angle is said to be positive.

Q. 3. When is the angle said to be negative?

Ans. If the direction of rotation of the given angle is clock-wise , then the angle is said to be negative.

Q. 4. Define radian ?

Ans. One radian is defined as the angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle.

Q. 5. How is radian related to degree measure of an angle ?

Ans.   1 Radian = 57^o16’21’’ = 57.27^o

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