NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

Class 11 Maths Ex 3.1 is the first exercise in the chapter on Trigonometric Functions. It teaches you how to measure angles using two main units: degrees and radians. You will learn the formulas to convert one into the other and solve problems about circles, rotating wheels, and swinging pendulums using the arc length formula.

Check Out: CBSE Class 11 Books

Below is the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.1:

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) 5π/3

(iv) 7π/6

Solution:

(i) 11/16 Here, π radian = 180°(ii) -4 Here, π radian = 180°(iii) 5π/3 Here, π radian = 180°We get = 300 ^o (iv) 7π/6 Here, π radian = 180°We get = 210 ^o

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 2π 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 at an angle of 12π 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 the minor arc of the chord.

Solution:

The dimensions of the circle are Diameter = 40 cm Radius = 40/2 = 20 cm Consider AB as the chord of the circle, i.e., length = 20 cmIn 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/rTherefore, the length of the minor arc of the chord is 20π/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 the radian through 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

Check out: CBSE Class 11 Question Bank

1. Basics of Class 11 Maths Ex 3.1

Before you start solving the sums, you need to understand the two ways we measure angles. Just like we can measure length in centimeters or inches, we can measure angles in degrees or radians. This section of class 11 Maths ex 3.1 solutions makes these rules very simple to follow.

• Degrees: This is what you usually use in school. A full circle is 360 degrees.

• Radians: This is a newer unit for many students. A full circle is  2\pi  radians.

• Minutes and Seconds: Degrees can be broken down further. 1 degree ( 1^\circ ) has 60 minutes ( 60' ), and 1 minute has 60 seconds ( 60'' ).

2. Main Formulas for Class 11 Maths Ex 3.1

To get the right class 11 Maths ex 3.1 NCERT solutions, you must know how to switch between units. Use these two simple math rules whenever you see a conversion question. They are the most important part of this exercise.

Converting Degrees to Radians

If the question gives you an angle in degrees and asks for radians, use this rule:

 \text{Radian Measure} = \frac{\pi}{180} \times \text{Degree Measure}  

For example, if you have  180^\circ , you multiply it by  \pi/180  to get  \pi  radians.

Converting Radians to Degrees

If the question gives you radians and asks for degrees, use the flip of that rule:

\text{Degree Measure} = \frac{180}{\pi} \times \text{Radian Measure}  

When you do this, you often use the value of  \pi  as  22/7  to get the final answer in degrees and minutes.

The Arc Length Rule

When an arc (a curved part of a circle) makes an angle at the center, we use the formula:

\theta = \frac{l}{r}  

•  \theta  (Theta): The angle at the center (it must be in radians).

•  l : The length of the arc.

•  r : The radius of the circle.

Check Out: CBSE Question Bank Class 11 Mathematics

3. Step-by-Step Class 11 Maths Ex 3.1 Solutions

Let’s look at how to solve the different types of problems found in your textbook. These steps follow the logic used in class 11 Maths ex 3.1 teachbook and other top guides to help you get full marks.

How to Change Units

1. Look at the given number: Is it in degrees or radians?

2. Pick your formula: Use  \pi/180  for radians or  180/\pi  for degrees.

3. Simplify the fraction: Cut the numbers down to the smallest possible size.

4. Handle Minutes: If you have minutes, divide them by 60 first to turn them into degrees before you convert.

Solving Word Problems

The exercise has cool problems about wheels and pendulums. For a wheel problem:

• Find how many times the wheel turns in one second.

• Multiply that number by  2\pi  because one full turn is  2\pi  radians.

• For a pendulum, remember that the length of the string is the radius (r) and the path it swings is the arc length (l).

4. Tips for Class 11 Maths Ex 3.1 Samacheer Kalvi

If you are following the class 11 Maths Ex 3.1 Samacheer Kalvi or CBSE patterns, you should keep these helpful tips in mind. They will prevent you from making small mistakes that cost points.

• Don't Forget Radians: In the formula  \theta = l/r , the angle  \theta  is always in radians. If the question gives it in degrees, change it to radians first!

• Use  22/7 : Only put this value in for  \pi when you are moving from radians to degrees. If the answer asks for radians, leave  \pi as it is.

• Draw a Circle: For questions about chords and arcs, draw a quick picture. It helps you see the triangle inside the circle.

• Check the Clock: Remember that the minute hand of a clock moves  360^\circ  in 60 minutes. This means it moves  6^\circ  every single minute.

5. Important Questions and Answers for Practice

Here are the most common types of questions you will find when looking for class 11 Maths Ex 3.1 NCERT solutions. Practice these to feel ready for your class tests.

Q1: Find the radian measure for  25^\circ .

Using our rule:  \frac{\pi}{180} \times 25 . After dividing by 5, we get  \frac{5\pi}{36}  radians.

Q2: A wheel makes 360 turns in 1 minute. How many radians does it turn in 1 second?

• In 60 seconds, it turns 360 times.

• In 1 second, it turns  360/60 = 6  times.

• One turn is  2\pi  radians. So, 6 turns is  6 \times 2\pi = 12\pi  radians.

Q3: Find the degree measure for  11/16  radians.

Multiply  11/16  by  180/\pi. Use  \pi = 22/7 . After doing the math, you get  39^\circ 22' 30'' .

Q4: If two circles have the same arc length but different angles, what happens?

You use the ratio l = r_1\theta_1 = r_2\theta_2. This helps you find the ratio of the radii of the two circles.

Read More: CBSE Class 11 Important Topics

Class 11 Maths Chapter 3 Exercise 3.1 FAQs 

1. What is the main goal of class 11 maths ex 3.1?

The main goal is to learn how to measure angles using degrees and radians and how to switch between them.

2. Can I find class 11 maths ex 3.1 solutions in Hindi?

Yes, many students use guides and videos to find these solutions explained in Hindi for better understanding.

3. Why do we use radians instead of degrees?

Radians are often used in higher math and science because they make formulas involving circles much simpler to solve.

4. Is class 11 maths ex 3.1 difficult for exams?

Not at all! Once you learn the two conversion formulas and the l = r\theta  rule, you can solve almost every question in this exercise.

5. Where can I find the class 11 maths ex 3.1 ncert solutions PDF?

You can find the PDF on many educational websites. It is good to have a copy to look at while you do your homework.