## NCERT Solutions for Maths Class 11 Chapter 3 Exercise 3.1 - FREE PDF Download

## FAQs on NCERT Solutions for Class 11 Maths Chapter 3 - Trigonometric Functions Exercise 3.1

**1. What will I learn in this chapter of class 11 maths chapter 3?**

Here, you will learn about Degree of measure, Angles, Radian measure, Relations between Radian and Real numbers, Relation between Degree and Radian, Trigonometric Functions, Sign of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles and Trigonometric Equations. All the topics will help to learn how to find the radian measure of degree measures, how to find the degree measures of a radian measure, how to find the ratio of the radii of a circle, how to find trigonometric functions in quadrants and many more calculations.

**2. Give anyone an illustrative example for trigonometry?**

Illustrations:

1. Tan^{-1}(−½) +
Tan-1 (−⅓) =
Tan-1 [(−½ − ⅓)/ (1− ⅙)]

= Tan-1(−1)

= −π/4

2. Tan-1(−2) + Tan-1(−3) = Tan-1[(−2+−3)/ (1−6)]

= Tan-1(−5/ −5) = Tan-1 1

= π/4

3. Tan-1 (−3) + Tan-1 (−⅓) = − ( Tan-1B) + Tan-1(⅓)

= −π/2

4. Tan-1(5/3) − Tan-1(¼) = Tan-1[(5/3−¼)/ (1+5/12)]

= Tan-1(17/17)

= Tan-11 = π/4

5. Tan-12x + Tan-13x = π/4

=
Tan-1[(5x)/ (1−6x^{2})] = π/4

= 5x/ (1−6x^{2}) = 1

⇒ 6x^{2} − 5x + 1 = 0

⇒ x = 1/6 or −1

∴ x = 16 as, x = −1

6. If Tan-1(4) + Tan-1(5) = Cot-1(λ). Find λ

Here,

Tan-1[9/ (1−20)] = Cot-1 λ

= Tan-1(-9/19) = Cot-1(λ)

= − Tan-1(9/19) = Cot-1(λ)

= − Cot-1 (19/9) = Cot-1(λ)

Or, λ = −19/9

**3. What are trigonometric identities?**

In earlier classes, we have studied the concept of ratio. We now define a particular ratio which involves the sides of a right angled triangle, and then call them as trigonometric ratios. This chapter also will introduce you to a few advanced concepts which are related to trigonometric identities, which are commonly the square terms of the functions. They are:

Sin

^{2}A + cos^{2}A = 11 + tan

^{2}A = sec^{2}A1 + cot

^{2}A = cosec^{2}A

Three proofs are presented concerning these expressions. These three expressions have a vast list of applications in different forms.

**4. What does property set 1 and property set 2 of trigonometry consists?**

Below are the sets of property 1 and 2:

Property Set 1:

Sin^{-1}(x) = cosec^{-1}(1/x), x∈ [−1,1]−{0}

Cos^{-1}(x) = sec^{-1}(1/x), x ∈ [−1,1]−{0}

Tan^{-1}(x) = cot-1(1/x), if x > 0 Or,

= cot^{-1}(1/x) −π, if x < 0

Cot^{-1}(x) = tan^{-1}(1/x), if x > 0 Or,

= tan^{-1}(1/x) + π, if x < 0

Property Set 2:

Sin^{-1}(−x) = −Sin^{-1}(x)

Tan^{-1}(−x) = −Tan^{-1}(x)

Cos^{-1}(−x) = π − Cos^{-1}(x)

Cosec^{-1}(−x) = − Cosec^{-1}(x)

Sec^{-1}(−x) = π − Sec^{-1}(x)

Cot^{-1}(−x) = π − Cot^{-1}(x)

You will also read about proofs of:

Sin

^{-1}(−x) = −Sin^{-1}(x)Cos

^{-1}(−x) = π − Cos^{-1}(x)

**5. What are the important concepts required to solve Class 11 Maths Exercise 3.1?**

The important concepts that you will require to learn in Class 11 Maths Chapter 3 Exercise 3.1 are the initial side and terminal side of an angle, different measures to calculate angle (degree measure and radian measure). If you have understood these concepts very clearly, you will be able to easily solve all the questions in Exercise 3.1. Use Vedantu’s official website or the Vedantu app for NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.1 to get comprehensive answers to the exercise at free of cost. These solutions have been written by experts in an easy to understand language to help you score good marks in exams.

**6. What study plan to follow for Class 11 Maths Exercise 3.1?**

Maths can seem like a tough subject, but if you have a study plan to strategize and organize your syllabus, you can overcome the biggest hurdles of time management and the vast syllabus of Class 11 Maths Exercise 3.1. The best study plan is to practise the sums every day and take the help of Vedantu for a detailed explanation. You can get access to Vedantu’s Study Plan for Class 11 Maths NCERT Solutions for Class 11 Maths Chapter 3 at free of cost. For Exercise 3.1, all you need to do is practise all the questions once and keep revising them to ensure you don’t forget the concepts.

**7. What is the initial side and terminal side?**

The initial side is the original ray from which the angle originates and the terminal side is the ray, on which the angle after rotating is finally positioned. For more simple explanations, you should check out the NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.1 on Vedantu to get the answers to the full 3.1 Exercise. Comprehensive answers have been provided by experts with miscellaneous questions and answers as well.

**8. Is class 11 Maths chapter 3 easy?**

Class 11 Chapter 3 can become easy for you if you have the correct mindset. You need to have the correct guidance to show you the best path. The best guide that you will find today is Vedantu. You can improve your score with Vedantu’s NCERT Solutions. You should use NCERT Solutions Class 11 Maths Chapter 3 to be able to solve this chapter. The simplistic nature of the solution will help you practice the exercises smoothly.

**9. How to score full marks in questions from Chapter 3 Class 11 Maths?**

Getting top scores in Class 11 Chapter 3 Maths may look like a tough job, but with Vedantu, the journey will be a smooth ride. With Vedantu, you will get the best study plan to organize your syllabus around a routine and the best NCERT Solutions Class 11 Maths to give you a clearer idea of all the concepts and exercises, including Chapter 3. All the exercises have been solved step wise so that everything is graspable.

10. What are the key formulas to remember for class 11 maths 3.1?

Key formulas include degree to radian conversion $Radians=Degrees\times \frac{\pi }{180}$ and radian to degree conversion $Degrees=Radians\times \frac{180}{\pi}$.

11. How can NCERT Solutions help with class 11 maths ch 3 ex 3.1?

NCERT Solutions offer detailed explanations and step-by-step solutions for each question, simplifying the understanding and solving of problems. These solutions enhance learning and exam preparation.