The chapter contains questions and concepts revolving around Trigonometric functions. Exercise 3.1 of NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions is based on the following topics:
- Introduction
- Angles
- Degree measure
- Radian measure
- Relation between radian and real numbers
- Relation between degree and radian
These solutions are helpful for the students to get an idea of how to answer the questions from the exam perspective. View online or download the NCERT solutions for class 11 to get a hold on all the concepts covered in the chapter.
Download PDF of NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Exercise 3.1
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Access other exercise solutions of Class 11 Maths Chapter 3- Trigonometric Functions
Exercise 3.2 Solutions 10 Questions
Exercise 3.3 Solutions 25 Questions
Exercise 3.4 Solutions 9 Questions
Miscellaneous Exercise On Chapter 3 Solutions 10 Questions
Access Solutions for Class 11 Maths Chapter 3.1 exercise
1. Find the radian measures corresponding to the following degree measures:
(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°
Solution:
(iv) 520°
2. Find the degree measures corresponding to the following radian measures (Use π = 22/7)
(i) 11/16
(ii) -4
(iii) 5Ï€/3
(iv) 7Ï€/6
Solution:
(i) 11/16
Here π radian = 180°
(ii) -4
Here π radian = 180°
(iii) 5Ï€/3
Here π radian = 180°
We get
= 300o
(iv) 7Ï€/6
Here π radian = 180°
We get
= 210o
3. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Solution:
It is given that
No. of revolutions made by the wheel in
1 minute = 360
1 second = 360/60 = 6
We know that
The wheel turns an angle of 2Ï€ radian in one complete revolution.
In 6 complete revolutions, it will turn an angle of 6 × 2π radian = 12 π radian
Therefore, in one second, the wheel turns an angle of 12Ï€ radian.
4. Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π = 22/7).
Solution:
5. In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Solution:
The dimensions of the circle are
Diameter = 40 cm
Radius = 40/2 = 20 cm
Consider AB be as the chord of the circle i.e. length = 20 cm
In ΔOAB,
Radius of circle = OA = OB = 20 cm
Similarly AB = 20 cm
Hence, ΔOAB is an equilateral triangle.
θ = 60° = π/3 radian
In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre
We get θ = 1/r
Therefore, the length of the minor arc of the chord is 20Ï€/3 cm.
6. If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Solution:
7. Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm (ii) 15 cm (iii) 21 cm
Solution:
In a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = 1/r
We know that r = 75 cm
(i) l = 10 cm
So we get
θ = 10/75 radian
By further simplification
θ = 2/15 radian
(ii) l = 15 cm
So we get
θ = 15/75 radian
By further simplification
θ = 1/5 radian
(iii) l = 21 cm
So we get
θ = 21/75 radian
By further simplification
θ = 7/25 radian
