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Trigonometry

Trigonometry. Test grades will be in Wed afternoon Test corrections Thu, Fri, Mon am and pm Retakes Thu , Fri , Mon pm ONLY Pick up trig packet.

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Trigonometry

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  1. Trigonometry

  2. Test grades will be in Wed afternoonTest corrections Thu, Fri, Mon am and pmRetakes Thu, Fri, Mon pm ONLYPick up trig packet

  3. 10/2 Test grades were posted Wed afternoonTest corrections Thu, Fri, Mon am and pmRetakes Thu, Fri, Mon pm ONLY. End of six weeks is FridayYesterday we reviewed trig. The notes are on line. We began the trig packetToday you will complete trig packet. It is due at the EOC.Pay attention to units: all sides must match! 1inch = 2.54 cm

  4. What does it mean to say “as the crow flies”?

  5. What does it mean to say “as the crow flies”?

  6. What is the Pythagorean Theorem? c2 = a2 + b2

  7. Side labels

  8. Name the sides J K L

  9. Name the sides J hyp K opp L adj

  10. SOH CAH TOA

  11. What does Sin θ stand for? • Ratio of Opposite / Hypotenuse for a given angle • What does Cos θ stand for? • Ratio of Adjacent / Hypotenuse for a given angle • What does Tan θ stand for? • Ratio of Opposite / Adjacent for a given angle

  12. Find the tan for the given angle • First name the sides • Tan = Opp/Adj = 11.2 cm/8.4 cm = 1.33 14 cm 8.4 cm 11.2 cm

  13. Use tan function to fin the tan (ie. The ratio) Tan (53.13º) Tan (53.13º) = 1.333

  14. Use inverse tan function to find the angle if Tanθ = 1.333 Tan-1(1.333) = 53.12º

  15. We have looked at: • Pythagoreans • Naming sides • Determining ratios • Determining sides • Determining angles

  16. Summary Ratios: sinθ , cosθ and tanθ describe ratio of two sides. No unit. • Can determine two ways(ex with sin): • Knowing the angle: sin(30º) = 0.5 • Knowing the sides: sin θ=Opp/Hyp sin θ =5m/10m = .5 10m 5m 30º

  17. Summary Angles: To find angles use the inverse of the appropiate function:sin-1 , cos-1 and tan-1 • Can determine two ways(ex with sin): • Knowing the sides: sin-1 (5m/10m)= 30º • Knowing the ratio: sin-1 (.5)= 30º 10m 5m 30º

  18. Summary Putting it all together: If you need to determine a side: • Name sides in reference to known angle • Determine formula You know angle and hypotenuse, want opposite: Opp = (sinθ)(Hyp) (sin30º)(10m) = 5m 10m hyp ?? opp 30º

  19. Summary Putting it all together: If you need to determine an angle : • Name sides in reference to angle of interest • Determine formula • You know opp and hypotenuse, want θ : sin-1 = (Opp/Hyp) • sin-1 (5m/10m)=30º 10m hyp 5m opp Θ ??

  20. 1. 32 m b B 32 m Sin 55° = 55º a B = (32 m)(sin 55°) = 26.21 m To solve for a… a = 18.36 m b = 26.21 m = 18.36 m

  21. 2. Find R and Ө.

  22. ? 50.m 35° Finding a sideThe Church Steeple Eric decides to find the height of the steeple of his local church. He measures a distance of 50. m along the ground. The angle of elevation of the top of the steeple is 35°in reference to the ground. How high is the steeple? Step 1. Draw a diagram.

  23. The Church Steeple Have the Adjacent side and an angle Want the Opposite side. Use tan q = opp/adj ? 35° 50m Opp = (tan q) (adj) Opposite= (tan 35°)(50m) = 35 m

  24. 30.m ? 500.m Finding An Angle The Airplane At Bush IAH airport there is a forest just 500. m from the end of the runway. The trees can be as tall as 30. m. What is the minimum angle of climb if aircraft are to avoid the trees? Step 1. Draw a diagram.

  25. Finding An Angle Have the Adjacent and Opposite sides Want the angle Use tan q = opp/adj To find angles need to use tan-1 30 q 500 • = tan-1 (30m/500m) • = 3.4º

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