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Super Trig PowerPoint

Super Trig PowerPoint. Introduction- Finding lengths. Sin, cos or tan to find lengths?. Finding Missing Angles. Finding lengths and angles (more practise). Finding missing lengths worksheet. The Sine rule. The Cosine Rule. The Sine and Cosine Rule (quiz and worksheet).

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Super Trig PowerPoint

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  1. Super Trig PowerPoint

  2. Introduction- Finding lengths Sin, cos or tan to find lengths? Finding Missing Angles Finding lengths and angles (more practise) Finding missing lengths worksheet The Sine rule The Cosine Rule The Sine and Cosine Rule (quiz and worksheet) The Sine rule proof The Cosine Rule proof Finding the Area of Triangles and Segments Trig graphs Trig graphs- matching cards Combining the Rules

  3. Use sin, cos and tan to find the missing lengths, round them to 1 d.p, and use that answer to work out the next length. 51˚ 30˚ 10cm i a 40˚ e 50˚ d b 45˚ 42˚ c f 27˚ g h 35˚ 38˚

  4. Use sin, cos and tan to find the missing lengths, round them to 1 d.p, and use that answer to work out the next length. 51˚ 30˚ 10cm i a 40˚ e 50˚ d b 45˚ 42˚ c f 27˚ g h 35˚ 38˚

  5. Home

  6. Trigonometry 1

  7. Warm up Solve the following equations: • 20= • 15= • 8= • 7= • 16= 32 X X 2 21 X X 3 64 X

  8. Trigonometry • We can use trigonometry to find missing angles and lengths of triangles. • Trigonometry uses three functions, these are called: • Sine (shortened to Sin and pronounced “sign”) • Cosine (shortened to Cos) • Tangent (shortened to Tan) • We will start working with right angled triangles

  9. Labelling the sides Before we can use Sin, Cos and Tan we need to be able to label the sides of a right angled triangle The longest side, the one opposite the right angle is called the hypotenuse Hypotenuse

  10. Labelling the sides What we call the other two sides will change depending on which angle we are working with, for example.. If we are given (or need to work out) this angle, we label the other sides like this.. Adjacent Opposite But if we are working with this angle, we label the sides like this... ϴ Opposite Adjacent

  11. Labelling Right Angle Triangle 10 multiple choice questions

  12. What is the side marked with an X? X ϴ Adjacent Opposite A) B) Hypotenuse C)

  13. What is the side marked with an X? ϴ X Hypotenuse Opposite A) B) Adjacent C)

  14. What is the side marked with an X? X ϴ Hypotenuse Opposite A) B) Adjacent C)

  15. What is the side marked with an X? ϴ X Opposite Adjacent A) B) Hypotenuse C)

  16. What is the side marked with an X? X ϴ Adjacent Opposite A) B) Hypotenuse C)

  17. What is the side marked with an X? X ϴ Opposite Adjacent A) B) Hypotenuse C)

  18. What is the side marked with an X? ϴ X Opposite Adjacent A) B) Hypotenuse C)

  19. What is the side marked with an X? ϴ X Opposite Hypotenuse A) B) Adjacent C)

  20. What is the side marked with an X? ϴ X Hypotenuse Adjacent A) B) Opposite C)

  21. What is the side marked with an X? X ϴ Hypotenuse Opposite A) B) Adjacent C)

  22. Sine (sin) 10cm We use Sine when we have the Opposite length and the Hypotenuse 5cm The rule we use is: Opposite Hypotenuse Sinϴ= Try entering sin30 in your calculator, it should give the same answer as 5 ÷ 10 30˚ 5 10 Sin30=

  23. Sin Example 1 We can use Sin as the question involves the Opposite length and the Hypotenuse 7cm O The rule we use is: Opposite Hypotenuse Sinϴ= O 7 Sin42= 42˚ 7 x Sin42= O 4.68 cm (2dp)= O

  24. Sin Example 2 We can use Sin as the question involves the Opposite length and the Hypotenuse H 10cm The rule we use is: Opposite Hypotenuse Sinϴ= 10 H Sin17= H x Sin17= 10 17˚ H= 10 Sin17 H= 34.2 cm (1dp)

  25. Cosine (cos) We use cosine when we have the Adjacent length and the Hypotenuse Hypotenuse The rule we use is: Adjacent Hypotenuse Cosϴ= Adjacent 50˚

  26. Cos Example 1 We can use Cos as the question involves the Adjacent length and the Hypotenuse 9cm The rule we use is: Adjacent Hypotenuse Cosϴ= A A 9 Cos53= 53˚ 9 x Cos53= A 5.42 cm (2dp)= A

  27. Cos Example 2 We can use Cos as the question involves the Adjacent length and the Hypotenuse H 9cm 17˚ The rule we use is: Adjacent Hypotenuse Cosϴ= 9 H Cos17= H x Cos17= 10 H= 9 Cos17 H= 9.41 cm (2dp)

  28. Tangent (tan) We use tangent when we have the Opposite and Adjacent lengths. 10cm The rule we use is: Opposite Adjacent Tanϴ= 6.4cm (1dp) 50˚

  29. Tan Example 1 We can use Tan as the question involves the Adjacent and Opposite lengths 11cm The rule we use is: Opposite Adjacent Tanϴ= O O 11 Tan53= 53˚ 11 x Tan53= O 14.6 cm (1dp)= O

  30. Tan Example 2 We can use Tan as the question involves the Adjacent and Opposite lengths A The rule we use is: 21cm Opposite Adjacent Tanϴ= 21 A Tan35= 35˚ A x Tan35= 21 A= 29.99 cm (2dp) A= 21 Tan35

  31. The three rules So we have: Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Sinϴ= Cosϴ= Tanϴ= O H A H O A Sinϴ= Cosϴ= Tanϴ= SOHCAHTOA There are a few ways to remember this

  32. Silly Old Horses Can’t Always Hear The Other Animals SOHCAHTOA WHAT?

  33. Practise • Use Sine to find the missing lengths on these triangles: 2. Use Cosine to find the missing lengths on these triangles: 3. Use Tangent to find the missing lengths on these triangles: H 15cm 60˚ O 50˚ 17cm Opposite Hypotenuse Sinϴ= Opposite Adjacent Adjacent Hypotenuse Tanϴ= Cosϴ= H 22cm 60˚ 25cm 38˚ A 60˚ A O 42˚ 11cm 15cm

  34. Home

  35. Trigonometry 2

  36. Skiers On Holiday Can Always Have The Occasional Accident SOHCAHTOA Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Sinϴ= Cosϴ= Tanϴ=

  37. Our aim today • We have looked at the three rules and have practised labelling triangles. • Today we will have to decide whether we are using Sin, Cos or Tan when answering questions.

  38. SOH CAH TOA This question will use Sine X 7 O H Sin35= Sinϴ= 7cm X Hypotenuse opposite 35˚

  39. SOH CAH TOA This question will use Tan O A Tanϴ= Adjacent 17˚ 8 X Tan17= X 8cm opposite

  40. SOH CAH TOA This question will use Sin O H Sinϴ= X 43˚ 8 X Sin43= Hypotenuse 8cm opposite

  41. SOH CAH TOA This question will use Cosine O A cosϴ= Adjacent 26˚ X 8 Hypotenuse cos26= 8cm X

  42. Sin, Cos or Tan? 10 multiple choice questions

  43. Will you use Sin, Cos or Tan with this question? 11cm X 35˚ Cos Sin A) B) Tan C)

  44. Will you use Sin, Cos or Tan with this question? 14˚ 15cm X Sin Tan A) B) Cos C)

  45. Will you use Sin, Cos or Tan with this question? X 40˚ 17cm Sin Cos A) B) Tan C)

  46. Will you use Sin, Cos or Tan with this question? 50˚ 5cm X Tan Sin A) B) Cos C)

  47. Will you use Sin, Cos or Tan with this question? X 51˚ 6cm Cos Tan A) B) Sin C)

  48. Will you use Sin, Cos or Tan with this question? X 16˚ 8cm Sin Tan A) B) Cos C)

  49. Will you use Sin, Cos or Tan with this question? X 42˚ 14cm Sin Cos A) B) Tan C)

  50. Will you use Sin, Cos or Tan with this question? X 35˚ 4cm Tan Cos A) B) Sin C)

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