Mathematics Lab Activity-9 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 - 9

Objective

To prepare a model to illustrate the values of sine and cosine functions for different angles which are multiples of  π/2 and π

Material Required

A stand fitted with 0^o to 360^o protractor and a circular plastic sheet fixed with handle which can be rotated at the centre of the protractor.

Theory

1.  Conversion of degree measure into radian measure. 

Angle in degree	0o	30o	45o	60o	90o	180o	270o	360o
Angle in radian	0o	π/6	π/4	π/3	π/2	π	3π/2	2π

2. Values of trigonometric functions :

Angle in radian	0o	π/6	π/4	π/3	π/2	π	3π/2	2π
Sinθ	0	1/2	1/√2	√3/2	1	0	-1	0
Cosθ	1	√3/2	1/√2	1/2	0	-1	0	1
Tanθ	0	1/√3	1	√3	Not defined	0	Not defined	0

Values of cotθ, secθ and cosec θ are the reciprocal of the above given values.

3.  Sign of trigonometric functions in different quadrants:

Quadrants	I	II	III	IV
Sinθ	+	+	-	-
cosθ	+	-	-	+
tanθ	+	-	+	-
cotθ	+	-	+	-
secθ	+	-	-	+
cosecθ	+	+	-	-

Procedure

1.  Take a  stand fitted with 0^o  to 360^o protractor.

2. Let the radius of the protractor be considered as 1 unit.

3. Draw lines, one joining 0^o to 180^o line and the other joining 90^o to 270^o line. These lines are XOX’ and YOY’ and are perpendicular to each other.

4. Mark the ends of 0^o – 180^o line as (1, 0) at 0^o and (-1, 0) at 180^o.

Fig. 9.1

5. Mark the ends of the  line as (0,1) at 90^o and (0,-1) at 270^o.

6. Take a circular plate of plastic and mark a line on it to indicate the radius and fix a handle at the outer end of the radius.

7. Fix this plastic circular plate at the centre of the protractor.

8. Rotate the circular plate in the anticlockwise direction to make different angles like    0, π/2, π, 3π/2, 2π  ……….. etc

9. Read the values of sine and cosine functions for these angles and their multiples and record them in a tabular form.

Observations

At 0^o  → sin0^o = 0 and cos0^o = 1

At  π/2 →sin π/2 = 1 and cos π/2= 0

At π →sinπ = 0 and cosπ = -1

At 3π/2→ sin 3π/2 = -1 and cos 3π/2 = 0

At 2π  → sin2π= 0, and cos 2π = 1

Angles   →	0	π/2	π	3π/2	2π	5π/2	3π	7π/2	4π
Sin	0	1	0	-1	0	1	0	-1	0
Cos	1	0	-1	0	1	0	-1	0	1

Result

sinnπ= 0, where n, 0, 1, 2, 3,…………………….

sin(2n + 1)π/2= 1 ; where n = 0, 2, 4, ………………

 sin(2n + 1)π/2= -1 ; where n = 1, 3, 5, ………………

cosnπ= 1 ; where n = 0, 2, 4, ………..

cosnπ= -1 ; where n = 1, 3, 5…….

cos(2n + 1)π/2 = 0 ; where n = 0, 1, 2, 3 ……….

Applications

With the help of this activity we can find the values of other trigonometric functions  with the multiples of   π/2 and π

VIVA – VOICE

Q. 1. Who started the use of the symbols sin^-1x, cos^-1x   etc.

Ans.  The astronomer Sir F. W. Harsehel.

Q. 2. What is the value of sin(2nπ+x)?

Ans. sinx

Q. 3. What is the value of cos(2nπ+x)?

Ans. cosx

Q. 5. What is the value of sin(31π/3)?

Ans. sin(31π/3)=sin(10π + π/3) = sin(π/3)=√3/2

Q. 6. What is the value of cos(-1710^o)?

Ans. cos(-1710^o) = cos(1710^o) = cos (1800^o-90^o) = cos90^o = 0

THANKS FOR YOUR VISIT

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