The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron', and it means ‘measuring the sides of a triangle’. The subject was originally developed to solve geometric problems involving triangles. Trigonometry is an essential section of mathematics; trigonometric functions and identities are used in solving most mathematical problems. If students don't have a clear understanding of this chapter, they will face trouble in solving questions of other chapters too. In class 10, basic knowledge of trigonometric identities and applications is already taught to students. In Class 11 trigonometry, students will learn about trigonometric ratios and functions and their properties. From an examination point of view also, this chapter is important.
Topics covered in the chapter: Trigonometric functions |
1. Introduction |
2. sequences |
3. series |
4. Arithmetic progression(A.P) |
5. Arithmetic mean |
6. Geometric progression (G.P) |
7. General term of a G.P |
8. Sum of n terms of a G.P |
9. Geometric mean (G.M) |
10. Relationship between A.M and G.M |
11. Sum of n terms of special series |
In this chapter, students will learn about various trigonometric functions and how to use them in solving mathematical problems. We will also be discussing sequences, series, arithmetic progression, and geometric progression, and other related topics.
Formulas of trigonometry class 11 |
1. cos2 x + sin2 x = 1 2. 1 + tan2 x = sec2 x 3. 1 + cot2 x = cosec2 x 4. cos (2nπ + x) = cos x 5. sin (2nπ + x) = sin x 6. sin (– x) = – sin x 7. cos (– x) = cos x 8. cos (x + y) = cos x cos y – sin x sin y 9. cos (x – y) = cos x cos y + sin x sin y 10. cos ( π 2 − x ) = sin x 11. sin ( π 2 − x ) = cos x 12. sin (x + y) = sin x cos y + cos x sin y 13. sin (x – y) = sin x cos y – cos x sin y 14. cos (π/2+ x ) = – sin x 15. cos (π – x) = – cos x 16. cos (π + x) = – cos x 17. cos (2π – x) = cos x 18. sin (π/ 2+ x ) = cos x 19. sin (π – x) = sin x 20. sin (π + x) = – sin x 21. sin (2π – x) = – sin x |
22. If none of the angles x, y and (x ± y) is an odd multiple of π 2, then tan(x+y) = tan x + tan y / 1-tan x tan y tan(x-y) = tan x + tan y / 1+ tan x tan y |
23. If none of the angles x, y and (x ± y) is a multiple of π, then cot (x + y) = cot x cot y - 1 / cot x + cot y cot (x – y) = cot x cot y - 1/ cot x - cot y |
24. cos 2x = cos^{2}x – sin^{2} x = 2cos^{2}x – 1 = 1 – 2 sin^{2}x = 1 - tan^{2} x / 1 +tan^{2} x |
25. sin 2x = 2 sin x cos x= 2 tan x/1+tan2x |
26. sin 3x = 3sinx – 4sin^{3}x |
27. cos 3x = 4cos^{3}x – 3cos x |
28. 2cos x cos y = cos ( x + y) + cos ( x – y) |
29. – 2sin x sin y = cos (x + y) – cos (x – y) |
30. 2sin x cos y = sin (x + y) + sin (x – y) |
31. 2 cos x sin y = sin (x + y) – sin (x – y) |
32. tan 3x = 3 tanx- tan^{3}x/1-3 tan^{2}x |
33. cos x + cos y = 2cos( x+y/2 )cos (x-y/2) |
34. cos x – cos y = – 2sin(x+y/2) sin (x-y/2 ) |