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Trigonometry Review

Trigonometry Review. 9/4 tutoring until 3:10 today You need a calculator everyday. Quiz first thing. Get out ½ piece of paper long ways. Record first and last name and period at top. Title it Unit I Qz. Number 1-15 down the side.

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Trigonometry Review

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  1. Trigonometry Review

  2. 9/4 tutoring until 3:10 todayYou need a calculator everyday. Quiz first thing. Get out ½ piece of paper long ways. Record first and last name and period at top. Title it Unit I Qz. Number 1-15 down the side. Pick up Trig notes and Yesterday we worked on metrics and dimensional analysis. For tomorrow complete any 5 of the first 6 DA problems s 02 Meas WS1. I would strongly suggest you include #4 Today is trig review. Remember to put your calculators away at the end of the period in the correct pocket. I am not your maid.

  3. 9/1 Yesterday we worked on solving right triangles Today’s goal: Practice solving right triangles using trig Periods 5-7: pick up Math Ref 04 (4th got this handout yesterday) Solve Now: One dime has the mass of 2.59 grams and a diameter of 17.9 mm. If these dimes are aligned edge to edge, how many kilometers would 1.0 mole of dimes cover? Assume that 1 mole of dimes = 6.02 x 1023 dimes. Tomorrow: Quiz over right triangles & dimensional analysis.

  4. 9/6 Turn in triangle WS to blue sorter. I will answer questions about DA and triangles, and then we will take quiz

  5. Cylinder Lab #3 The expected relationship between circumference /diameter is pi. IF c = 2лr and d=2r THEN c/d is 2лr/2r = л

  6. One dime has the mass of 2.59 grams and a diameter of 17.9 mm. If these dimes are aligned edge to edge, how many kilometers would 1.0 mole of dimes cover? Assume that 1 mole of dimes = 6.02 x 1023 dimes.

  7. Convert moles to km.

  8. Convert moles to km.

  9. What is the difference between the following? • Perimeter • Area • Circumference

  10. What is the difference between the following? • Perimeter • Total length of outer boundary of a figure • L+W+L+W • Area • Measure of bounded region on a plane • L x W (rectangle) • Circumference • The line bounding a circle • 2лr

  11. Radius • Distance from center to periphery of a circle • Hypotenuse • Side of right triangle opposite the 90 angle

  12. We will be focusing on triangles

  13. Ex A: What is the area of triangle A? A= ½ bh A= ½(3.00u)(6.00u) A= 9.00 u2 6 3

  14. Ex B: What is the measure triangle A’s hypotenuse? a2 + b2 = c2 3.002 + 6.002 = c2 c = 6.71 u 6 3

  15. Ex C: Given the following triangle C a = 4.21u b = 7.43 u Angle C = 90.0° What is c? c = 8.54 u b c a

  16. a = 4.21u b = 7.43 u c = 8.54 u Same triangle C What is measure of smallest angle, A? A b c a

  17. SOH CAH TOA • This is a good time to review SOH CAH TOA • Sine = opposite / hypotenuse • Cosine = adjacent / hypotenuse • Tangent = opposite / adjacent • These only work for right triangles!

  18. What’s this SOHCAHTOA? What does sine, cosine, and tangent represent?

  19. What’s this SOHCAHTOA? What does sine, cosine, and tangent represent? Table The proportionality constant between given sides of a right triangle in reference to a specific angle.

  20. Naming the sides This side is oppositeour angle. This is the longest side— the hypotenuse. H O A right angled triangle A This side is adjacentto our angle. The angle weare interested in.

  21. Naming the sides O H A H A O H A O A H A O H O H = Hypotenuse O = Opposite A = Adjacent

  22. Sine Let’s check if the angle is really 30° H = O = 30° 8cm 4cm Here we know the Hypotenuse and the Oppositeside. So we use the Sine function. This tells us that sin 30° = 4/8 = 0.5. You can check with a calculator that sin 30° is 0.5.

  23. If O/H is .5 How do I get the angle? • Sin-1(4/8)

  24. a = 4.21u b = 7.43 u c = 8.54 u Same triangle What is measure of smallest angle, A? Sin θ = opp/hyp Sin θ = 4.21/8.54 θ = 29.5° A c b a

  25. a = 4.21u b = 7.43 u c = 8.54 u Same triangle Can I find measure of smallest angle, A with another function? Cos θ = adj/hyp Cos θ = 7.43/8.54 θ = 29.5° A b c a

  26. How would you determine the last angle? • We will use trig, not geometry. ☺

  27. Complete triangles D and E on bottom of pg 2 of unit 02 trig review.

  28. Ex D: A right triangle D has sides with measurements of 7.48, 15.0, and 13.0 units. What is the measure of the hypotenuse? What is the measure of the largest UNKNOWN angle of such triangle? What is the measure of the smallest angle? • Hypotenuse = 15 u • Largest angle = 60.1° • Smallest angle = 29.9°

  29. Ex E: A right triangle E has a hypotenuse measuring 28.0 u. One angle has a measure of 22.0°. What is the measure of the smallest side? What is the measure of the remaining side? What is the measure of the remaining angle? • Side a = 10.5u • Side b = 26.0 u • Angle θ = 68.0°

  30. Refer to table on notes page: • What can be said of the sine value of an angle as that angle’s size increases? • increases • What can be said of the cosine value of an angle as that angle’s size increases? • decreases • As the cosine value of an angle decreases, the sine value of that same angle increases.

  31. 9/9 Thursday • Goal: Assess understanding of dimensional analysis and solving right triangles • Introduce Law of Sines and Cosines • Have your homework out so we can check it!

  32. 9/10 Friday • Goal: Introduce Law of Sines and Cosines • If you were absent yesterday you will be taking the Trig/DA Quiz during class. You will be responsible for getting any missed notes and will be required to complete the homework assignment. • HW: Oblique Triangles

  33. Tests are available to be viewed on Test Correction Days. • Test corrections will earn you a daily grade • Retakes (For Quizzes and Tests with less than a 70 average) : • You must have completed your review sheet before the test. • You must perform test corrections • You must have all class notes and assignments completed. This must be shown to me for approval. • Failure to comply negates retake eligibility. • You must fill out a retake appointment sheet 24 hours in advance. Failure to show at scheduled time voids your option for retake. • Corrections and retakes must be performed within 5 days of receiving the graded assignment and are available only during after school tutoring days unless otherwise noted. (Mon-Wed 2:35 -3:15) • I am available this Friday and next Monday and Tuesday.

  34. Quizzes are graded but not in gradebook yet. Please return them to lue sorter or get a zero.

  35. Given the following triangle G a = 7.20u b = 4.35u One angle is 95° How do you solve this triangle?

  36. Law of Cosines • Useful when know side-angle-side or side-side-side • Law of Cosines a2 = b2 +c2 – [2bc cosA] b2 = a2 +c2 – [2ac cosB] c2 = a2 +b2 – [2ab cosC]

  37. Law of Cosines a2 = b2 +c2 – [2bc cosA] b2 = a2 +c2 – [2ac cosB] c2 = a2 +b2 – [2ab cosC] • If you know the adjacent sides on any angle you can determine the third side

  38. a2 = b2 +c2 – [2bc cosA]Solve for cosA a2 = b2 +c2 – [2bc cosA] cosA = [a2 - b2 -c2 ]/[-2bc] If you know all the sides you can determine any angle. You just have to rearrange the appropriate law and solve for the angle.

  39. Triangle F. First Draw and label Sides in lower cases Angles in upper case and across for corresponding side. Can use law of cosines to determine c c2 = a2 +b2 – [2ab cosC] A b c 95° C a B

  40. Triangle F a = 7.20u b = 4.35 uc2 = a2 +b2 – [2ab cosC] c2 = (7.20u)2 + (4.35u)2 – [2(7.20u)(4.35u)(cos95°)] c2 = 76.2 c = 8.73u

  41. Triangle F. Know sides and one angle. How to determine the other angles? a = 7.20u b = 4.35 u c = 8.73u C = 95° Use Law of Sines a/sinA = b/sinB = c/sinC A b c 95° C a B

  42. a = 7.20u • b = 4.35 u • c = 8.73u C = 95° a/sinA = b/sinB = c/sinCWhat is angle A? a/sinA = c/sinC solve for sin A sin A = [a(sinC)] ÷ c sin A = [(7.20u) (sin 95°)] ÷ 8.73u Sin A = 0.822 A = 55.2°

  43. Triangle F. Know sides and two angles. How to determine the last angle? a = 7.20u A = 55.2° b = 4.35u c = 8.73u C = 95° Remember a triangle equals 180° 180°- (55.2° + 95°) B = 29.8° A b c 95° C a B

  44. Some things to remember • Angles in a parallelogram total 360o • SOH CAH TOA for right triangles only • Pythagorean Theorem (for right triangles): a2 + b2 = c2 • Law of Cosines a2 = b2 +c2 – [2bc cosA] b2 = a2 +c2 – [2ac cosB] c2 = a2 +b2 – [2ab cosC] • Law of Sines a/sinA = b/sinB = c/sinC B a c C b A

  45. Beware: • Law of Sines has problem when solving for angles above 100. It is okay to use if you know the side corresponding to an angle above 100. But if the angle you are solving for could be over 100, use the law of cosines. Add your total angles up to check!

  46. Consider a triangle G with the following measures: B = 85.0° a = 4.00 b = 6.00 Determine A, C, and Side c. What would you solve for first? A = C = c =

  47. Consider a triangle G with the following measures: B = 85.0° a = 4.00 b = 6.00 Determine A, C, and Side c. What would you solve for first? A = 41.6° C = 53.4° c = 4.84

  48. Consider a triangle H with the following measures: C = 103° B = 16° c = 12 Determine A, Side a, and Side b. What would you solve for first? A = a = b =

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