Trigonometry 2
- 1. Trigonometry
- 2. 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.
- 3. Trigonometric Ratios SOHCAHTOA Sine Ɵ = opposite__ hypotenuse Cosine Ɵ = adjacent__ hypotenuse Tangent Ɵ = opposite adjacent
- 4. Example 2 Find the value of angles Ɵ and λ in triangle LMN. 13m 12m 5m θ λ
- 5. 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
- 6. 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
- 7. Example 3 Find the value of angles QPR and RQP and the length of the side PR. 7m 6m Q P R
- 8. 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
- 9. 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
- 10. 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
- 11. 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.