The document provides an overview of the history and development of trigonometry. It discusses how trigonometry originated in ancient Greece and Mesopotamia for applications in astronomy and was further developed by Greek mathematicians such as Hipparchus. Key concepts in trigonometry like trig functions, trig identities, and trig ratios are also explained.

1. WELCOME

3. HARILAL KRISHNA VISHNU K N AMITH KUMAR SANOOJ SAURAV S K Trigonometry

4. WHICH SO OCCUPIES THERE IS PERHAPS NOTHING THE MIDDLE POSITION OF MATHEMATICS AS TRIGONOMETRY - J.F.HERBART

9. Who am I? I was credited for preparing tables of sines used for solving problems in astronomy and a Greek mathematician of antiquity introduced trigonometry as a systematized body of knowledge. “ I am the eight letter of the alphabet + the symbol of the imaginary number + double the first letter of polynomial + (3a-2a) +r + c + the inverse of “n” + 20 th letter-1”

10. YES, I am Hipparcus of Bithynia (190-120 B.C.)

17. TRIGONOMETRIC RATIOS

19. TRIGONOMETRIC RATIOS

24. Opposite side: the side opposite the angle angle angle angle opposite opposite opposite opposite angle

25. Adjacent side: the side beside the angle adjacent adjacent adjacent adjacent angle angle angle angle

26. Hypotenuse: the longest side hypotenuse hypotenuse hypotenuse hypotenuse

27. b c Two shorter sides squared and added together equal to the longest side

28. The sine of an angle is the ratio of the opposite side to the hypotenuse side. SOH opposite hypotenuse

29. Sine of angle A A B 90 o C a c b sin( A ) = = a c opposite hypotenuse

30. Sine of angle B A B 90 o C a c b sin( B ) = = b c opposite hypotenuse

31. The cosine of an angle is the ratio of the adjacent side and hypotenuse side. CAH adjacent hypotenuse

32. Cosine of angle A A B 90 o C a c b cos( A ) = = b c adjacent hypotenuse

33. Cosine of angle B A B 90 o C a c b cos( B ) = = a c adjacent hypotenuse

34. The tangent of an angle is the ratio of the opposite side and adjacent side. TOA opposite adjacent

35. Tangent of angle A A B 90 o C a c b tan( A ) = opposite adjacent a b =

36. Tangent of angle B A B 90 o C a c b tan( B ) = opposite adjacent b a =

37. Solving Real-Life Problems A steel rod is used to support a tree which is in danger of falling down. What is the length of the rod? When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem to calculate its length. 15m 8m rod

38. Calculating the Hypotenuse Aeroplane b = 8 a = 15 c Edappal Airport Q1. An aeroplane is preparing to land at kozhikode Airport. It is over Edappal at present which is 15km from the airport. It is at a height of 8km. How far away is the plane from the airport? Example 2

39. Example 1 Find all the angles x, where 0 < x < 4 π where sin x = 0.5 Principle value: Using symmetry: Using periodicity:

40. The two angles Angle of Elevation The word “elevation” means “rise” or “move up”. Angle of elevation is the angle between the horizontal and the line of sight to an object above the horizontal. Angle of Depression The word “depression” means “fall” or “drop”. Angle of depression is the angle between the horizontal and the line of sight to an object beneath the horizontal.

41. HARILALKRISHNA