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Trigonometry

Trigonometry. Trigonometry can be used for two things: 1. Using 1 side and 1 angle to work out another side, or 2. Using 2 sides to work out an angle. Sin, Cos and Tan. To work out things using trigonometry we use three new buttons on the calculator labelled. Sin Cos Tan

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Trigonometry

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  1. Trigonometry

  2. Trigonometry can be used for two things: 1. Using 1 side and 1 angle to work out another side, or 2. Using 2 sides to work out an angle.

  3. Sin, Cos and Tan To work out things using trigonometry we use three new buttons on the calculator labelled. Sin Cos Tan Each of these buttons has a rule you can remember by using the word: SOH-CAH-TOA

  4. SOH-CAH-TOA In this word each letter stands for a word. Buttons on your calculator Sides of a Triangle S = Sin A = Adjacent C = Cos O = Opposite T = Tan H = Hypotenuse

  5. The Hypotenuse is the longest side. It is the one not touching the right angle. Hypotenuse Hypotenuse Hypotenuse

  6. The Opposite is the side far away from the angle you are given. 60o Opposite 30o Opposite

  7. Opposite Opposite 57o 33o

  8. The Adjacent is the side next to the angle you are given. 60o Adjacent 30o Adjacent

  9. 41o Adjacent 49o Adjacent

  10. Sin Sin (full name sine) has the rule SOH. Theta means an angle. O H Sin θ

  11. Cos Cos (full name cosine) has the rule CAH. A H Cos θ

  12. Tan Tan (full name tangent) has the rule TOA. O A Tan θ

  13. Steps • Label the sides of the triangle. • Figure out which type of side you are looking for and which sides you have. • Write down the formula from SOH-CAH-TOA. • Put in the numbers. • Calculate. • If you are trying to find an angle you need to press: = Sin Shift = or Cos Shift = or Tan Shift

  14. Hypotenuse 24 We are looking for the Opposite. We have the Hypotenuse. We need to use SOH because it has O and H. O = Sin θ × H y = Sin 30 × 24 y = 12 Opposite y 30o Adjacent

  15. Hypotenuse 15 We are looking for the Opposite. We have the Hypotenuse. We need to use SOH because it has O and H. O = Sin θ × H y = Sin 48 × 15 y = 11.1 Opposite y 48o Adjacent

  16. Hypotenuse 20 We are looking for the Adjacent. We have the Hypotenuse. We need to use CAH because it has A and H. A = Cos θ × H y = Cos 28 × 20 y = 17.7 Opposite 28o y Adjacent

  17. 40o Hypotenuse Adjacent We are looking for the Opposite. We have the Adjacent. We need to use TOA because it has O and A. A = Tan θ × A y = Tan 40 × 23 y = 19.3 23 y Opposite

  18. Opposite 6.0 Adjacent We are looking for the Hypotenuse. We have the Opposite. We need to use SOH because it has O and H. H = O ÷ Sin θ y = 6.0 ÷ Sin 40 y = 9.3 40o y Hypotenuse

  19. 50o Hypotenuse 100 Adjacent We are looking for the Adjacent. We have the Hypotenuse. We need to use CAH because it has A and H. A = Cos θ × H y = Cos 50 × 100 y = 64.3 y Opposite

  20. Hypotenuse We are looking for the Opposite. We have the Adjacent. We need to use TOA because it has O and A. O = Tan θ × A y = Tan 32 × 1.4 y = 0.9 Opposite y 32o 1.4 Adjacent

  21. Opposite Adjacent We are looking for the Hypotenuse. We have the Adjacent. We need to use CAH because it has A and H. H = A ÷ Cos θ y = 32.5 ÷ Cos 40 y = 42.4 32.5 40o y Hypotenuse

  22. Opposite 3.2 Adjacent We are looking for the Adjacent. We have the Opposite. We need to use TOA because it has O and A. A = O ÷ Tan θ y = 3.2 ÷ Tan 40 y = 3.8 y 40o Hypotenuse

  23. θ Adjacent 7 Hypotenuse 4 We are looking for an angle. We have the Adjacent and the Hypotenuse. We need to use CAH because it has A and H. Cos θ = A ÷ H Cos θ = 4 ÷ 7 Cos θ = 0.57 Opposite = Cos Shift θ = 55o

  24. θ Adjacent 10 Hypotenuse We are looking for an angle. We have the Hypotenuse and the Opposite. We need to use SOH because it has O and H. Sin θ = O ÷ H Sin θ = 8 ÷ 10 Sin θ = 0.8 8 Opposite = Sin Shift θ = 53o

  25. θ Adjacent 10 Hypotenuse 5 We are looking for an angle. We have the Hypotenuse and the Adjacent. We need to use CAH because it has A and H. Cos θ = A ÷ H Cos θ = 5 ÷ 10 Cos θ = 0.5 Opposite = Cos Shift θ = 60o

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