Class 11 Maths Chapter 3 Trigonometric Functions – Exercise 3.3 NCERT Solutions

Introduction

Exercise 3.3 focuses on solving trigonometric equations. You will learn how to find general solutions of equations involving sine, cosine, tangent, and other trigonometric functions. This exercise builds the foundation for solving higher‑order trigonometric problems in calculus and advanced mathematics.

Key Concepts

1. General Solution of Sine Equation:

$$\sin \theta =\sin \alpha ⟹\theta =n\pi +(-1{)}^n\alpha ,n\in \mathbb{Z}$$

2. General Solution of Cosine Equation:

$$\cos \theta =\cos \alpha ⟹\theta =2n\pi \pm \alpha ,n\in \mathbb{Z}$$

3. General Solution of Tangent Equation:

$$\tan \theta =\tan \alpha ⟹\theta =n\pi +\alpha ,n\in \mathbb{Z}$$

NCERT Questions with Solutions (10)

Q1. Solve $\sin \theta =\frac{\sqrt{3}}{2}$.

$$\theta =n\pi +(-1{)}^n\frac{\pi }{3},n\in \mathbb{Z}$$

Q2. Solve $\cos \theta =\frac{1}{2}$.

$$\theta =2n\pi \pm \frac{\pi }{3},n\in \mathbb{Z}$$

Q3. Solve $\tan \theta =1$.

$$\theta =n\pi +\frac{\pi }{4},n\in \mathbb{Z}$$

Q4. Solve $\sin \theta =0$.

$$\theta =n\pi ,n\in \mathbb{Z}$$

Q5. Solve $\cos \theta =0$.

$$\theta =\frac{\pi }{2}+n\pi ,n\in \mathbb{Z}$$

Q6. Solve $\tan \theta =0$.

$$\theta =n\pi ,n\in \mathbb{Z}$$

Q7. Solve $\sin \theta =1$.

$$\theta =\frac{\pi }{2}+2n\pi ,n\in \mathbb{Z}$$

Q8. Solve $\cos \theta =-1$.

$$\theta =\pi +2n\pi ,n\in \mathbb{Z}$$

Q9. Solve $\tan \theta =\sqrt{3}$.

$$\theta =n\pi +\frac{\pi }{3},n\in \mathbb{Z}$$

Q10. Solve $\cot \theta =0$.

$$\theta =\frac{\pi }{2}+n\pi ,n\in \mathbb{Z}$$

FAQs (10)

1. What is general solution of sine equation? $\theta =n\pi +(-1{)}^n\alpha$.

2. What is general solution of cosine equation? $\theta =2n\pi \pm \alpha$.

3. What is general solution of tangent equation? $\theta =n\pi +\alpha$.

4. What is domain of sine function? All real numbers.

5. What is range of sine function? $[-1,1]$.

6. What is domain of cosine function? All real numbers.

7. What is range of cosine function? $[-1,1]$.

8. What is domain of tangent function? All real numbers except odd multiples of $\frac{\pi }{2}$.

9. What is range of tangent function? $\mathbb{R}$.

10. Why is this exercise important? It builds skills in solving trigonometric equations systematically.

Conclusion

Exercise 3.3 has 10 solved questions and 10 FAQs that strengthen your understanding of solving trigonometric equations. This builds the foundation for advanced trigonometric problem solving in Class 11 Maths.

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