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Week 1 - Trigonometry

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Mi primera semana de clases de mi curso de Trigonometría.

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Week 1 - Trigonometry

  1. 1. Day 11.Course Guidelines2. Critical Path to Success
  2. 2. Critical Path to Success!!A student who wants to succeed in this course will: • Always be on time for class.
  3. 3. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed.
  4. 4. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed.
  5. 5. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Notebooks
  6. 6. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Notebooks
  7. 7. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Pencil Notebooks
  8. 8. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Pencil Notebooks
  9. 9. Critical Path to Success!!A student who wants to succeed in this course will: • Always arrive to class prepared to work with all the materials needed. Pencil Notebooks Pen(s)
  10. 10. Critical Path to Success!!A student who wants to succeed in this course will: • Always attempt ALL their homework assignments.
  11. 11. Critical Path to Success!!A student who wants to succeed in this course will: • Review their class notes every night before going to bed.
  12. 12. The Curve of Forgetting... Describes how we retain or get rid of information that we take in. It´s based on a one-hour lecture.
  13. 13. Critical Path to Success!!A student who wants to succeed in this course will: • Always ask LOTS of questions about anything they don’t understand.
  14. 14. Critical Path to Success!!A student who wants to succeed in this course will: • Always gets extra help from the teacher when they feel they are falling behind.
  15. 15. 3. Opener 2 a) What polynomial do you subtract from 3x − 8 to get 5x −10 ? b) Distribute: −2x 2 (4 x 5 − 5) c) Simplify:€ € 4 2 5 −2 ⎛10x ⎞−3 € (5x ) (5x ) ⎜ 3 ⎟ ⎝ 5x ⎠ d) What does Manero’s Steakhouse in Greenwich, CN, offer to € any baby born in the restaurant? €
  16. 16. Day 21. Opener.1. What is the first step in any factoring problem?2. What is the first step to factor -x2 + 8x - 15?3. On a test, Luis Gonzalez wrote the following, but the teacher considered it to be incomplete. Explain why 15x2 - 21x - 18 = (5x + 3)(3x - 6)4. What appetizer is most requested with a last meal?
  17. 17. 2. Factoring Review.
  18. 18. Before we start...
  19. 19. Before we start...1. What is a prime number?
  20. 20. Before we start...1. What is a prime number?2. What’s factoring?
  21. 21. Before we start...1. What is a prime number?2. What’s factoring?3. Why do we need factoring?
  22. 22. 3. Factoring Strategy.Step 1. Always check for the _____________________ first.
  23. 23. 3. Factoring Strategy. greatest common factorStep 1. Always check for the _____________________ first.
  24. 24. Step 2.Is the expression a -termed expression? If yes, then try one of these three forms: 1. _______________________________: 2. _______________________________: 3. _______________________________:
  25. 25. Step 2.Is the expression a two -termed expression? If yes, then try one of these three forms: 1. _______________________________: 2. _______________________________: 3. _______________________________:
  26. 26. Step 2.Is the expression a two -termed expression? If yes, then try one of these three forms: a2 - b2 = (a + b)(a - b) 1. _______________________________: 2. _______________________________: 3. _______________________________:
  27. 27. Step 2.Is the expression a two -termed expression? If yes, then try one of these three forms: a2 - b2 = (a + b)(a - b) 1. _______________________________: a3 + b3 = (a + b)(a2 - ab + b2) 2. _______________________________: 3. _______________________________:
  28. 28. Step 2.Is the expression a two -termed expression? If yes, then try one of these three forms: a2 - b2 = (a + b)(a - b) 1. _______________________________: a3 + b3 = (a + b)(a2 - ab + b2) 2. _______________________________: a3 - b3 = (a - b)(a2 + ab + b2) 3. _______________________________:
  29. 29. Step 3.If it is a -termed expression (or trinomial), it may fall into one of these groups: 1.The coefficient of is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  30. 30. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: 1.The coefficient of is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  31. 31. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: 1.The coefficient of x is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  32. 32. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  33. 33. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. Find two -17 numbers whose sum is ______ and whose product is ______. They are ______ and ______:
  34. 34. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. Find two -17 numbers whose sum is ______ and whose product is ______. -60 They are ______ and ______:
  35. 35. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. Find two -17 numbers whose sum is ______ and whose product is ______. -60 -20 They are ______ and ______:
  36. 36. Step 3.If it is a three -termed expression (or trinomial), it may fall into one of these groups: x2 - 17x - 60 1.The coefficient of x is 1. Example: ________________. Find two -17 numbers whose sum is ______ and whose product is ______. -60 -20 3 They are ______ and ______:
  37. 37. 2. The coefficient of is not 1. Example: ________________. a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  38. 38. 2. The coefficient of x is not 1. Example: ________________. a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  39. 39. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  40. 40. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  41. 41. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ -18 = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  42. 42. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ -18 = _____. -18 b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  43. 43. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ -18 = _____. -18 b. Look for two numbers whose product is ______ and whose -7 sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  44. 44. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ -18 = _____. -18 b. Look for two numbers whose product is ______ and whose -7 -9 sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  45. 45. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ -18 = _____. -18 b. Look for two numbers whose product is ______ and whose -7 -9 sum is _____: _____ and ______. 2 c. Write the expression as four terms: d. Proceed to use Step 4 as follows:
  46. 46. 6x2 - 7x - 32. The coefficient of x is not 1. Example: ________________. (6)(-3) a. Find the product of first and last coefficients: ___________ -18 = _____. -18 b. Look for two numbers whose product is ______ and whose -7 -9 sum is _____: _____ and ______. 2 c. Write the expression as four terms: 6x2 - 9x +2x - 3 d. Proceed to use Step 4 as follows:
  47. 47. Step 4.If it is a -termed expression, try factoring by grouping. Example:
  48. 48. Step 4.If it is a four-termed expression, try factoring by grouping. Example:
  49. 49. Step 4.If it is a four-termed expression, try factoring by grouping. Example: 2x2 - 3xy - 4x + 6y
  50. 50. 4. ExercisesFactor each expression completely. 4 2 3 1. x − 9x 2. x − 27 3 2 3. x + 8 4. 4t + 16t + 16 2 2 5. y − 9y + 20 6. 6m + 5m − 4
  51. 51. Homework 1.Baldor, Algebra:Exercise 106, Problems 9, 18, 27, 36, 47, 54, 73, 83, 91, 98, 109and 128, p. 171
  52. 52. Day 31. OpenerA person is standing at the top of a building, and throws aball upwards from a height of 60 ft, with an initial velocityof 30 ft per second. How long will it take for the ball toreach a height of 25 ft from the floor? 1 2Use the formula h = − gt + v0t + h0 2
  53. 53. 2. Quadratic FormulaIf ax2 +bx + c = 0 and a ≠ 0, then 2 −b ± b − 4ac x= 2a
  54. 54. 3. Exercises.Solve the equations: 2 1. y + 3y + 2 = 0 2 2. 2m + 3m − 35 = 0 2 3. 9b = −12b − 4 2 4. 2x − 6x − 5 = 0 2 5. 2x − 5x + 1 = 0
  55. 55. Day 41. Opener1. True or False:a) A function is a set of ordered pairs.b) A relation is a set of ordered pairs where the firstelement of each ordered pair is never repeated.2. What is the most recognizable ad icon of the 20thcentury?
  56. 56. Are the following relations functions, or just relations?
  57. 57. Are the following relations functions, or just relations? f = {(1, 2), (3, 4), (5, 6)}
  58. 58. Are the following relations functions, or just relations? f = {(1, 2), (3, 4), (5, 6)} f = {(3, 3), (3, 2), (4, 3)}
  59. 59. Are the following relations functions, or just relations? f = {(1, 2), (3, 4), (5, 6)} f = {(3, 3), (3, 2), (4, 3)}
  60. 60. Are the following relations functions, or just relations? f = {(1, 2), (3, 4), (5, 6)} f = {(3, 3), (3, 2), (4, 3)}
  61. 61. Are the following relations functions, or just relations? f = {(1, 2), (3, 4), (5, 6)} Relations f = {(3, 3), (3, 2), (4, 3)}
  62. 62. Are the following relations functions, or just relations? f = {(1, 2), (3, 4), (5, 6)} Relations f = {(3, 3), (3, 2), (4, 3)} Functions
  63. 63. Are the following relations functions, or just relations?
  64. 64. Are the following relations functions, or just relations? Vertical Line Test. Sweep a vertical line across the graph of the function. If the line crosses the graph more than once it is not a function, only a relation.
  65. 65. Day 71. Domain and Range.What is the domain and range of the following function?
  66. 66. Day 71. Domain and Range.What is the domain and range of the following function? Domain. Is the set of "input" or argument values for which the function is defined.
  67. 67. Day 71. Domain and Range.What is the domain and range of the following function? Domain. Is the set of "input" or argument values for which the function is defined. Range. Refers to the output of a function.
  68. 68. What is the domain and range of the following function?
  69. 69. 2. Examples.What is the domain and range of the following functions? 1. f (x) = 4 − x 1 2. g(x) = 2x + 3 3. y = 1− 2x
  70. 70. Day 51. Quiz 1.
  71. 71. 1. Quiz 1.Factor the following, completely: 21. x − 3x − 402. 2x 2 + 3x − 35 23. x − 49 24. z + 12z + 36 35. x + 8Use the cuadratic formula to solve: 25x − 2x + 7 = 0

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