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Trigonometry 2
 

Trigonometry 2

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    Trigonometry 2 Trigonometry 2 Presentation Transcript

    • Trigonometry
    • Lesson Objectives
      • Calculate the value of angles in a right angled triangle using trigonometric ratios.
      • Apply trigonometry to perform calculation checks.
      • Calculate the length of a side in a right angled triangle using trigonometric ratios.
    • Trigonometric Ratios
      • SOHCAHTOA
      • Sine Ɵ = opposite__
      • hypotenuse
      • Cosine Ɵ = adjacent__
      • hypotenuse
      • Tangent Ɵ = opposite
      • adjacent
    • Example 2
      • Find the value of angles Ɵ and λ in triangle LMN.
      13m 12m 5m θ λ
    • Example 2
      • Sin Ɵ = Opp = 12 = 0.923
      • Hyp 13
      • Ɵ = Sinˉ¹0.923
      • Ɵ = 67.38º
      • Sin λ = Opp = 5 = 0.385
      • Hyp 13
      • λ = 22.62º
    • Trigonometry Check
      • Check:180º - 90° - 67.38° = 22.62°
      • Sin λ = 22.62°
      • Cos λ = 12 = 0.923 Cos λ = 22.62°
      • 13
      • Tan λ = 5 = 0.416 Tan λ = 22.62°
      • 12
    • Example 3
      • Find the value of angles QPR and RQP and the length of the side PR.
      7m 6m Q P R
    • Example 3
      • Find angle QPR
      • Sin QPR = Opp = 6
      • Hyp 7
      • Sin QPR = 0.857
      • QPR = Sinˉ¹0.857
      • QPR = 59º
      7m 6m Q R P
    • Example 3
      • Find angle RQP
      • Cos RQP = Adj = 6
      • Hyp 7
      • Cos RQP = 0.857
      • RQP = Cosˉ¹0.857
      • RQP = 31º
      7m 6m Q P R
    • Example 3
      • RQP = 31° PQ = 7m
      • Sin RQP = Opp = PR
      • Hyp PQ
      • Sin 31° = PR
      • 7
      • PR = 7 x Sin 31° 7 x 0.515
      • PR = 3.6m
    • Lesson Objectives
      • Calculate the value of angles in a right angled triangle using trigonometric ratios.
      • Apply trigonometry to perform calculation checks.
      • Calculate the length of a side in a right angled triangle using trigonometric ratios.