Class 10 Maths Chapter 8 Introduction to Trigonometry – Exercise 8.2 NCERT Solutions

Introduction

Exercise 8.2 focuses on the trigonometric ratios of standard angles (0°, 30°, 45°, 60°, 90°). These values are derived using geometry of equilateral and isosceles right triangles. This exercise builds the foundation for solving trigonometric problems quickly without calculation.

Formula Used

• Standard Trigonometric Values:

θ	sin θ	cos θ	tan θ	cot θ	sec θ	csc θ
0°	0	1	0	∞	1	∞
30°	1/2	√3/2	1/√3	√3	2/√3	2
45°	1/√2	1/√2	1	1	√2	√2
60°	√3/2	1/2	√3	1/√3	2	2/√3
90°	1	0	∞	0	∞	1

NCERT Questions with Solutions (10)

Q1. Find sin 30°, cos 30°, tan 30°.

Solution: $\sin 30\mathrm{°}=\frac{1}{2},\cos 30\mathrm{°}=\frac{\sqrt{3}}{2},\tan 30\mathrm{°}=\frac{1}{\sqrt{3}}$.

Q2. Find sin 45°, cos 45°, tan 45°.

Solution: $\sin 45\mathrm{°}=\frac{1}{\sqrt{2}},\cos 45\mathrm{°}=\frac{1}{\sqrt{2}},\tan 45\mathrm{°}=1$.

Q3. Find sin 60°, cos 60°, tan 60°.

Solution: $\sin 60\mathrm{°}=\frac{\sqrt{3}}{2},\cos 60\mathrm{°}=\frac{1}{2},\tan 60\mathrm{°}=\sqrt{3}$.

Q4. Find sin 90°, cos 90°, tan 90°.

Solution: $\sin 90\mathrm{°}=1,\cos 90\mathrm{°}=0,\tan 90\mathrm{°}=\mathrm{\infty }$.

Q5. Find sin 0°, cos 0°, tan 0°.

Solution: $\sin 0\mathrm{°}=0,\cos 0\mathrm{°}=1,\tan 0\mathrm{°}=0$.

Q6. Find cot 30°, sec 30°, csc 30°.

Solution: $\cot 30\mathrm{°}=\sqrt{3},\sec 30\mathrm{°}=\frac{2}{\sqrt{3}},\csc 30\mathrm{°}=2$.

Q7. Find cot 45°, sec 45°, csc 45°.

Solution: $\cot 45\mathrm{°}=1,\sec 45\mathrm{°}=\sqrt{2},\csc 45\mathrm{°}=\sqrt{2}$.

Q8. Find cot 60°, sec 60°, csc 60°.

Solution: $\cot 60\mathrm{°}=\frac{1}{\sqrt{3}},\sec 60\mathrm{°}=2,\csc 60\mathrm{°}=\frac{2}{\sqrt{3}}$.

Q9. Find cot 90°, sec 90°, csc 90°.

Solution: $\cot 90\mathrm{°}=0,\sec 90\mathrm{°}=\mathrm{\infty },\csc 90\mathrm{°}=1$.

Q10. Find cot 0°, sec 0°, csc 0°.

Solution: $\cot 0\mathrm{°}=\mathrm{\infty },\sec 0\mathrm{°}=1,\csc 0\mathrm{°}=\mathrm{\infty }$.

FAQs (10 from NCERT)

1. Q: What are standard angles in trigonometry? A: 0°, 30°, 45°, 60°, 90°.

2. Q: Why are these values important? A: They simplify trigonometric calculations.

3. Q: How is sin 30° derived? A: From an equilateral triangle split into two right triangles.

4. Q: How is sin 45° derived? A: From an isosceles right triangle.

5. Q: What is tan 45°? A: 1.

6. Q: What is cos 60°? A: 1/2.

7. Q: What is sin 90°? A: 1.

8. Q: What is cos 0°? A: 1.

9. Q: Can tan 90° be defined? A: No, it is infinite.

10. Q: Why is this exercise important? A: It builds foundation for trigonometric identities and equations.

Conclusion

Exercise 8.2 has 10 solved questions and 10 FAQs that strengthen your understanding of trigonometric ratios of standard angles. This builds the foundation for advanced trigonometry in Class 10 Maths.

Visit: www.fuzymathacademy.com