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Junior Cert TRIGONOMETRY

Junior Cert TRIGONOMETRY. Some considerations. Make sure the calculator is in Degree Mode (DRG button) Practice getting the sine/cos/tan of various angles Inverse functions: [ 2 nd F button ] Use of backets is important when finding inverses: e.g . SECTION 1 . RIGHT ANGLED TRIANGLES.

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Junior Cert TRIGONOMETRY

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  1. Junior Cert TRIGONOMETRY

  2. Some considerations • Make sure the calculator is in Degree Mode (DRG button) • Practice getting the sine/cos/tan of various angles • Inverse functions: [2nd F button] Use of backets is important when finding inverses:e.g

  3. SECTION 1 RIGHT ANGLED TRIANGLES

  4. RIGHT ANGLED TRIANGLES A HYPOTHENUSE HYPOTHENUSE OPPOSITE ADJACENT 900 A 900 ADJACENT OPPOSITE

  5. c a b PYTHAGORAS THEOREM a2 +b2 = c2 The square of the hypotenuse is equal to the sum of the squares on the other 2 sides. This theorem is used when you are looking for the length of one side of a triangle when you are given the measurements of the other 2 sides. ( Remember this theorem only works for right angled triangles).

  6. Hypotenuse [H]

  7. Hypotenuse [H] Opposite [O] A Adjacent [A]

  8. A Hypotenuse [H] Adjacent [A] Opposite [O]

  9. A H O H O A Cosine Cos A = [H] [O] Sine Sin A = A Tangent [A] Tan A = SOHCAHTOA

  10. [5] [3] [4] [H] [O] A [A] O 3 SOHCAHTOA Sin A = = H 5

  11. [5] [3] A [4] [H] [O] [A] A 4 SOHCAHTOA Cos A = = H 5

  12. [5] [O] A [4] [H] [3] [A] O 3 SOHCAHTOA Tan A = = A 4

  13. [13] [12] A [5] [H] [O] [A] O 12 SOHCAHTOA Sin A = = H 13

  14. [13] [12] A [5] [H] [O] [A] A 5 SOHCAHTOA Cos A = = H 13

  15. [13] [12] A [5] [H] [O] [A] O 12 SOHCAHTOA Tan A = = A 5

  16. [15] x 300 x 0.5 = 15 1 O Looking for x H Given [H] [O] O x Sin 300 = = H 15 Sin 300 = 0.5 [A] SOHCAHTOA x = 15(0.5) = 7.5

  17. x 500 x 1.1917 = [15] 15 1 O Looking for x A Given [H] [O] O x tan 50o = = A 15 Tan 50o = 1.1917 [A] SOHCAHTOA x = 15(1.1918) = 17.876

  18. H x 35o 16’ 15 0.8164 = [15] 1 x Looking for x A Given A 15 [H] Cos 35o 16’ = = [O] H x Cos 35o 16’ = 0.8164 [A] x(0.8165) = 15 SOHCAHTOA 15 = 18.37 x = 0.8165

  19. THE ANGLE OF ELEVATION AND DEPRESSION (a) Angle of depression = Angle looking down (b) Angle of elevation = Angle looking up depression elevation

  20. QUESTIONS ON RIGHT ANGLED TRIANGLES Example 1 A plane takes of at an angle of 200 to the level ground. After flying for 100m how high is it off the ground. 100m height 900 200

  21. 100m HYP opp height 900 200 In this we are given the Hyp. And we are looking for the Opp So we use the Sin Formula

  22. 14m 10m

  23. 10m 8m

  24. Hyp = 13 x Adj = 5 Note: If given ratio always draw right angled triangle

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