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Trigonometry

Welcome to. Trigonometry. World. Presented by Nalini Harbhajan kaur Maths Mistress Pb Mistress G.H.S G.S.S.S Rohajri Naugajja. Objectives. To make the students familiar with term trigonometry ,uses of it ,basic formulas of it.

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Trigonometry

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  1. Welcome to Trigonometry World Presented by Nalini Harbhajan kaur Maths Mistress Pb Mistress G.H.S G.S.S.S Rohajri Naugajja

  2. Objectives • To make the students familiar with term trigonometry ,uses of it ,basic formulas of it. 2. To create interest of students in it. 3.To make teaching oftrigonometry effective.

  3. What is Trigonometry It is an important branch of mathematics It is drived from to Greek words *Trigonon meaning a triangle and *metron meaning measurement. Thus the word trigonometry means the science which deals with the measurement of triangle.

  4. Trigonometry helps us in calculating remaining sides and angles of right angled triangle. Knowledge of trigonometry has been used extensively in Astronomy ,Surveying ,Geography , Navigation , Physicaland Engineering Sciences etc. Uses of Trigonometry

  5. A h p Θ B b C PHYTHAGOROUS THEOREM • In righted triangle ABC right angled at B. • h2 = p2 + b2 Where h= hypotenuse • p=perpendicular b=base

  6. A Θ B C Explanationabout sides of triangle. • Let Θ be acute angle in right angled triangle ABC right angled at B. 1. AB is opposite side to angle Θ . . 2. BC is adjacent side to angle Θ. 3 .AC is hypotenuse.

  7. What is T-ratio or Trigonometric ratio. • Some ratio of different sides of a right triangle called T-ratio or Trigonometric ratio e.g .Sine,Cosine.

  8. A h p Θ C B b Sine of an angle. • The ratio AB\AC is called the Sine of angle Θ.In short it is written as Sin Θ. • Sin Θ = AB/AC • =opposite side/hypotenuse • = p/h

  9. A h p Θ b B C Cosine of an angle. • The ratio BC/AC is called the cosine of angle Θ. In short it is written as Cos Θ. • Cos Θ = BC/AC • =adjacent side/hypotenuse • = b/h

  10. A h p Θ b B C Tangentof an angle • The ratio AB/BC is called the tangent of angle Θ.In short it is written as Tan Θ. • Tan Θ = AB/BC • = opposite side/adjacent side • = p/b bb

  11. A h p Θ b B C RELATION BETWEENSin Θ Cos Θ and Tan Θ Sin Θ = p/h………..(1) Cos Θ = b/h……….(2) On dividing (1) by (2) We get Sin Θ\ Cos Θ = p/b = Tan Θ (As We know Tan Θ =p/b) ∴ Sin Θ /Cos Θ = Tan Θ

  12. A h p Θ B b C Cosecant of an angle • The ratio AC/AB is called Cosecant of an angle Θ.In short it is written as Cosec Θ. • Cosec Θ = hypotenuse/opposite side • = AC/AB • =h/p

  13. A h p Θ b B C Secant of an angle • The ratio AC/BC is called Secant of angle Θ.In short it is written as SecΘ. • Sec Θ =hypotenuse /adjacent side • = AC/BC • =h / b

  14. A h p Θ b B C Cotangent of an angle • The ratio BC/AC is called Cotangent of angle Θ.In short it is written as Cot Θ. • Cot Θ =adjacent side/opposite side • = BC/AC • =b / p

  15. A h p Θ B b C Relation among T-ratio • Tan Θ =Sin Θ/Cos Θ • Cosec Θ =1/Sin Θ • Sec Θ =1/Cos Θ • Cot Θ =Cos Θ /Sin Θ • = 1/Tan Θ

  16. POPULAR SONG TO LEARN • SARAE CHELAE TERE • PANDIT BADRI PARSAD • HAR HAR BOLE • IN short it is written as • S C T • P B P • H H B

  17. A h p Θ B b C Table • 1.Sin Θ = p/ h • 2.Cos Θ = b/ h • 3.Tan Θ = p/ b • 4.Cosec Θ = h/ p • 5.Sec Θ = h/ b • 6.Cot Θ = b/ p

  18. T RATIO OF SOME SPECIFIC ANGLES • Θ 0 0 30 0 450 600 900 Sin Θ 0 1/2 1/√2 √ 3/2 1 • Cos Θ 1 √ 3/2 1/√2 1/2 0 • Tan Θ 0 1/√3 1 √3 1/0 Cosec Θ 1//0 2 √ 2 2/√3 1 • Sec Θ 1 2/√3 √ 2 2 1/0 • Cot Θ 1/0 √ 3 1 1/√3 1

  19. Relation of Θwith Sin Θwhen 0 0<= Θ<= 900 • The greater the value of Θ, the greater is the value of Sin Θ. • Smallest value of Sin Θ= 0 • Greatest value of Sin Θ= 1

  20. Relation ofΘwithCos Θwhen0 0 <= Θ<= 900 • The greater the value of Θ , the smaller the value of Cos Θ. • Smallest value of Cos Θ=0 • Greatest value of Cos Θ= 1

  21. Relation of Θ with Tan ΘWhen 0 0 <=Θ <= 900 • Tan Θ increases as Θ increases but • Tan Θ is not defined (1/0) at Θ = 900 • Smallest value of Tan Θ = 0

  22. A h p Θ B b C Some More Formulae • If 00<= Θ <=900 • 1.Sin(900- Θ) = Cos Θ • 2.Cos(900- Θ) = Sin Θ

  23. A h p Θ B b C Some More Formulae • If 00< Θ <=900 Tan(900- Θ) = Cot Θ .If 00<= Θ <900 Cot(900- Θ)= Tan Θ

  24. A h p Θ B b C IDENTITIES IN TRIGNOMETRY • 1. Sin2Θ+Cos2Θ =1 • 2. Sec2 Θ -Tan2 Θ =1 • 3.Cosec2 Θ -Cot2 Θ =1

  25. A h p Θ B b C Some More Formulas • If 00<Θ<=900 Sec(900-Θ) = CosecΘ • If 00<=Θ<900 • Cosec(900-Θ) = SecΘ

  26. + A LOT OF THANX DIET PRINCIPAL and INSTRUCTOR PARVEEN KUMAR

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