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SOH-CAH-TOA EAST OF JAVA

SOH-CAH-TOA EAST OF JAVA. [Exploring Trigonometric Functions]. SOH-CAH-TOA means many things. “Hello” “Goodbye” “I love you” “Your slip is showing” “It’s Your turn to take out the trash!!!”. SOHCAHTOA Also Means: “Let’s do Trig!!. [SOH] Sine – Opposite – Hypotenuse

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SOH-CAH-TOA EAST OF JAVA

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  1. SOH-CAH-TOA EAST OF JAVA [Exploring Trigonometric Functions] Army Daniel

  2. SOH-CAH-TOA means many things • “Hello” • “Goodbye” • “I love you” • “Your slip is showing” • “It’s Your turn to take out the trash!!!” Army Daniel

  3. SOHCAHTOA Also Means: “Let’s do Trig!! [SOH] Sine – Opposite – Hypotenuse [CAH] Cosine – Adjacent – Hypotenuse [TOA] Tangent – Opposite - Adjacent Army Daniel

  4. First: A quick Geometry Review PARTS OF A RIGHT TRIANGLE OPPOSITE HYPOTENUSE ADJACENT Army Daniel

  5. So, Sohcahtoa![…trans. “Let’s do Trig.!”] Army Daniel

  6. We’ll break it into syllables. Army Daniel

  7. SOH-CAH-TOA Army Daniel

  8. SOH: SINE-OPP-HYP sin  = opposite side hypotenuse OPPOSITE HYPOTENUSE ADJACENT Army Daniel

  9. SOH-CAH-TOA Army Daniel

  10. CAH: COSINE-ADJ-HYP cos  = adjacent side hypotenuse OPPOSITE HYPOTENUSE ADJACENT Army Daniel

  11. SOH-CAH-TOA Army Daniel

  12. TOA: TAN-OPP-ADJ tan  = opposite side adjacent OPPOSITE HYPOTENUSE ADJACENT Army Daniel

  13. A QUICK REVIEW SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side Hypotenuse TOA - tan  = Opposite side Adjacent side Army Daniel

  14. APPLICATIONS: Let’s solve a problem. Sohcahtoa! Army Daniel

  15. Check for Understanding. Find sin  = cos  = tan  = 5 3 4 Army Daniel

  16. Check : Don’t Forget! Find sin  = OPP HYP cos  = ADJ HYP tan  = OPP ADJ 3 ADJ 5 HYP 4 OPP Army Daniel

  17. Check : ANSWERS Find sin  = OPP = 4 HYP 5 cos  = ADJ = 3 HYP 5 tan  = OPP = 4 ADJ 3 3 ADJ 5 HYP 4 OPP Army Daniel

  18. APPLICATIONS: Let’s try a different problem. Sohcahtoa! Army Daniel

  19. Check for Understanding. Find x given: cos 60° = 0.5 x 60° 1 Army Daniel

  20. Check for Understanding. Find x given: cos 60° = 0.5 And don’t forget SOH-CAH-TOA x 60° 1 Army Daniel

  21. Check : ANSWER X = 2 How? x 60° 1 Army Daniel

  22. Check : ANSWER X = 2 How? Use SOH – CAH - TOA cos 60° = .5 = ADJ = 1 HYP x .5x = 1 x = 2 x 60° 1 Army Daniel

  23. APPLICATIONS: Let’s try a WORD problem! Sohcahtoa! Army Daniel

  24. Find the Height of Mt. Sohcahtoa The volcano is rumbling. The Sohcahtoans need to sacrifice a virgin. They know the base of the mountain is 6 miles high. The angle formed from the base to the top is 60°. How tall is the mountain? [Use your calculator!!!] Army Daniel

  25. Find the Height of Mt. Sohcahtoa What do we know? • = 60° Base = 6 miles = 3 miles 2 Height 6 miles Army Daniel

  26. What else do know? SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side Hypotenuse TOA - tan  = Opposite side Adjacent side Which one should we use? Height 6 miles Army Daniel

  27. Which one? SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side Hypotenuse TOA - tan  = Opposite side Adjacent side Height 6 miles Army Daniel

  28. WHY?? tan  = Opposite side Adjacent side tan 60°(3mi) = h .(3mi) 3 mi (tan 60°)(3 miles) = h (0.866)(3) = h h = 2.598 miles Height h 3 miles Army Daniel

  29. WHY?? tan  = Opposite side Adjacent side tan 60°(3mi) = h .(3mi) 3 mi (0.866 )(3 miles) = h answer h = 2.598 miles Height h= 2.598 3 miles Army Daniel

  30. WHY?? tan  = Opposite side Adjacent side tan 60° = h . 3 miles (tan 60°)(3 miles) = h (0.866)(3) = h h = 2.598 miles Height h 3 miles Army Daniel

  31. WHY?? tan  = Opposite side Adjacent side tan 60° = h . 3 miles (tan 60°)(3 miles) = h (0.866)(3) = h h = 2.598 miles Height h 3 miles Army Daniel

  32. EXCELLENT!!! You deserve a HAND! Now, Let’s Work!!! SOHCAHTOA!!! Army Daniel

  33. Class Asignment: pp. 356-359 Problems #’s 1 – 40 Homework: p. 360 – 361 #’s 3 – 51 multiples of 3 ASSIGNMENT Army Daniel

  34. Resources • Picture of Sohcahtoa: [Devil’s Tower] http://www.animationfactory.com/free/nature/nature_page_aa.html Army Daniel

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