Matematika - Persamaan Trigonometri Sederhana
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Matematika - Persamaan Trigonometri Sederhana Presentation Transcript

  • 1. Trigonometry SIMPLE EQUATION
  • 2. Trigonomentri simpleequation is an equation that contains thecomparison trigonomentri
  • 3. In general, to solvetrigonometry is used in the following formula:
  • 4. 1. sin x = sin α x = α + k.360⁰ atau x = (180⁰ - α) + k.360⁰
  • 5. 2. cos x = cos αx = α + k.360⁰ atau x = - α + k.360⁰
  • 6. 3. tan x = tan α x = α + k.180⁰
  • 7. For angle in units of radians, in use the following formula:
  • 8. 1. sin x = sin α x = α + k.2π or x = (π – α) + k.2π
  • 9. 2. cos x = sin αx = α + k.2π or x = -α + k.2π
  • 10. 3. tan x = tan α x = α + k.π
  • 11. Example - exampleproblems trigonometric equations:
  • 12.  Determine the set of equations following the completion of the interval 0 ≤ x ≤ 2πa. Sin x = ½ √3b. Tan x = √3
  • 13. Answer :a. Sin x = ½√3 = sin (π/3 + k. 2π) x = π/3 + k. 2π for k = 0 x = π/3
  • 14. ORsin x = ½ √3 = sin ( π – π/3 + k.2π) x = 2π/3 + k . 2π For k = 0 x = 2π/3
  • 15. Thus, the solution set = {π / 3, 2π / 3}
  • 16. tan x = √3 = tan (π/3 + k. π) x = π/3 + k . πFor k = 0 x = π/3 + k.Π k=1 x = 4π/3
  • 17. so, the solution set = {Π / 3, 4π / 3}
  • 18. 2. Determine the set of completion of the equation cos (3x - 45 ⁰) = - ½ √ 2, for 0 ⁰ ≤ x ≤ 360 ⁰.
  • 19. Answer : Cos (3x – 45⁰) = -½√2 Cos (3x – 45⁰) = cos 135⁰ 3x – 45⁰ = 135⁰ + k. 360⁰ 3x = 180⁰ + k. 360⁰ x = 60⁰ + k. 120⁰ x = 60⁰ , 180⁰ , 300⁰
  • 20. OR3x – 45⁰ = -135 + k . 360⁰ 3x = -90⁰ + k . 360⁰ x = -30⁰ + k . 120⁰ x = 90⁰ , 210⁰ , 330⁰
  • 21. Thus, the solution set = {60 ⁰, 90 ⁰, 180 ⁰, 210 ⁰, 300 ⁰, 330 ⁰}
  • 22. The basic technique is to solvetrigonometric equations using trigidentities and algebra techniques totransform a trigonometric equation intosimpler forms.
  • 23. example:Determine the set ofcompletion of sin x = sin 70°,0° <x <360 °
  • 24. Answer : x = 70° + k.360° k = 0 ==> x = 70° atau x = (180 - 70) + k.360° ==> x=110° + k.360° k = 0 ==> x = 110° Jadi, Hp = {70°, 110°}
  • 25. Determine the set ofcompletion of cos x = cos 24in the interval 0 ° <x <360 °
  • 26. Answer : x = 24° + k.360° k = 0 , x = 24° OR x = -24° + k.360° k = 1 , x = -24° + 360° = 336° Thus, Hp = {24°, 336°}
  • 27. Determine the set of completion of tan x = tan 56 °, in the interval 0 ° <x <360 °
  • 28. Answer: x = 56 ° + ° k.180 k = 0 ==> x = 56 ° k = 1 ==> x = 56 ° + 180 ° = 236 ° Thus, the solution set is {52 °, 236 °}
  • 29. THANK YOU