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BY SIBY SEBASTIAN PGT(MATHS)

TRIGONOMETRIC FUNCTIONS BASIC IDEAS. BY SIBY SEBASTIAN PGT(MATHS). Basic Terms. A. C. B. Angle Measures and Types of Angles. Types of angles named on basis of measure:. Measuring Angles. Radian Measure. Comments on Radian Measure. Conversion Between Degrees and Radians.

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BY SIBY SEBASTIAN PGT(MATHS)

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  1. TRIGONOMETRIC FUNCTIONSBASIC IDEAS BY SIBY SEBASTIAN PGT(MATHS) siby sebastian pgt maths

  2. Basic Terms A C B siby sebastian pgt maths

  3. Angle Measures and Types of Angles Types of angles named on basis of measure: siby sebastian pgt maths

  4. Measuring Angles siby sebastian pgt maths

  5. Radian Measure siby sebastian pgt maths

  6. Comments on Radian Measure siby sebastian pgt maths

  7. Conversion Between Degrees and Radians siby sebastian pgt maths

  8. Convert Degrees to Radians a) 60 b) 221.7 221.70 = siby sebastian pgt maths

  9. Convert Radians to Degrees a) = x = b) 3.25 rad 3.25 rad = x siby sebastian pgt maths

  10. Equivalent Angles in Degrees and Radians siby sebastian pgt maths

  11. Trigonometric Functions In a circle of radius ‘r’ units and if P(x,y) is a point on the circle then the trigonometric functions are defined by sincosec cossec tancot = r y x siby sebastian pgt maths

  12. Trigonometric Functions siby sebastian pgt maths

  13. Exponential Notation and Trigonometric Functions • sin2 A = (sin A)2 • tan3A = (tanA)3 • Sec5A = (secA)5 siby sebastian pgt maths

  14. Signs of Trig Functions by Quadrant of Angle • Considering the following three functions and the sign of x, y and r in each quadrant, which functions are positive in each quadrant? siby sebastian pgt maths

  15. Mnemonic Techniques siby sebastian pgt maths

  16. Domain and Range of Sine Function siby sebastian pgt maths

  17. GRAPH OF sine FUNCTION Click here to see how sin function is generated siby sebastian pgt maths

  18. Domain and Range of Cosine Function siby sebastian pgt maths

  19. GRAPH OF cosine FUNCTION Click here to see how cosine function is generated siby sebastian pgt maths

  20. Domain and Range of Tangent Function siby sebastian pgt maths

  21. GRAPH OF tangent FUNCTION Click here to see how tangent function is generated siby sebastian pgt maths

  22. Domain and Range of Cosecant Function siby sebastian pgt maths

  23. GRAPH OF cosecant FUNCTION siby sebastian pgt maths

  24. Domain and Range of Secant Function siby sebastian pgt maths

  25. GRAPH OF secant FUNCTION siby sebastian pgt maths

  26. Domain and Range of Cotangent Function siby sebastian pgt maths

  27. GRAPH OF cotangent FUNCTION siby sebastian pgt maths

  28. Ranges of Trigonometric Functions For any angle  for which the indicated functions exist: Note that sec  and csc are never between 1 and 1 siby sebastian pgt maths

  29. Periodic Properties siby sebastian pgt maths

  30. Theorem Even-Odd Properties siby sebastian pgt maths

  31. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 1.sin( 2.cos() = sinx 3.tan( = cotx siby sebastian pgt maths

  32. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 4.sin( 5.cos() = - sinx 6.tan( = - cotx siby sebastian pgt maths

  33. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 7.sin( 8.cos() = -cosx 9.tan(= - tanx siby sebastian pgt maths

  34. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 10.sin( 11.cos() = -cosx 12.tan( = tanx siby sebastian pgt maths

  35. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 13.sin( 14.cos() = -sinx 15.tan( = cotx siby sebastian pgt maths

  36. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 16. sin( 17 .cos() = sinx 18 .tan( = - cotx siby sebastian pgt maths

  37. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 19.sin( 20.cos() = cosx 21.tan(2 =-tanx siby sebastian pgt maths

  38. BASIC RULES OF TRIGONOMETRIC FUNCTIONS • sin2x +cos2x =1 • 1+tan2x =sec2x • 1+cot2x =cosec2x siby sebastian pgt maths

  39. BASIC RULES OF TRIGONOMETRIC FUNCTIONS SUM AND DIFFERENCE OF TWO ANGLES 1.cos(x + y) = cosxcosy – sinxsiny 2.cos(x – y) = cosxcosy + sinxsiny 3.sin(x + y) = sinxcosy + cosxsiny 4.sin( x – y) = sinxcosy - cosxsiny siby sebastian pgt maths

  40. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 5.tan(x + y) = 6.tan(x – y) = 7.cot(x + y) = 8.cot(x - y) = siby sebastian pgt maths

  41. BASIC RULES OF TRIGONOMETRIC FUNCTIONS PRODUCT AS SUM OR DIFFERENCE 1 .2sinxcosy = sin(x + y) + sin(x – y) 2. 2cosxsiny = sin(x + y) – sin(x – y) 3.2cosxcosy = cos(x + y)+cos(x – y) 4.-2sinxsiny = cos(x + y) – cos(x – y) siby sebastian pgt maths

  42. BASIC RULES OF TRIGONOMETRIC FUNCTIONS SUM OR DIFFERENCE AS PRODUCT 1.sinx + siny = 2sin( 2.sinx – siny = 2cos( 3.cosx + cosy = 2cos( 4.cosx – cosy = - 2sin( siby sebastian pgt maths

  43. BASIC RULES OF TRIGONOMETRIC FUNCTIONS MULTIPLE ANGLES 1.sin2x = 2sinxcosx = 2.cos2x = cos2x – sin2x = 2cos2x – 1 = 1 – 2sin2x = siby sebastian pgt maths

  44. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 3.tan2x = 4.sin3x = 3sinx – 4sin3x 5.cos3x = 4cos3x – 3cosx 6.tan3x = siby sebastian pgt maths

  45. BASIC RULES OF TRIGONOMETRIC FUNCTIONS SUB MULTIPLE ANGLES 1.sinx = 2sin 2.cosx = 3.1- cosx = 2 4.1+cosx = 2 siby sebastian pgt maths

  46. BASIC RULES OF TRIGONOMETRIC FUNCTIONS GENERAL SOLUTIONS 1.sinx =0 then x= n, n 2.cosx = 0 then x=(2n + 1) n 3.tanx =0 then x= n, n siby sebastian pgt maths

  47. BASIC RULES OF TRIGONOMETRIC FUNCTIONS 4.Sinx = sinythen,x = n 5.cosx =cosy then 6.tanx = tany then x= n siby sebastian pgt maths

  48. BASIC RULES OF TRIGONOMETRIC FUNCTIONS Sine Rule siby sebastian pgt maths

  49. BASIC RULES OF TRIGONOMETRIC FUNCTIONS Cosine Rule cosA = cosB = cosC = siby sebastian pgt maths

  50. Finally let us dance together and enjoy trigonometry Practice Practice & Practice Until you get it. …….. siby sebastian pgt maths

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