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Chapter 7        Analytic TrigonometryMatthew 19:25-26When the disciples heard this, they were greatlyastonished and asked...
Chapter 7          Analytic TrigonometryMuch of this chapter will be new topics for you.  Read your textbook! Study the ex...
7.1 Trigonometric Identities
7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.
7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.An equatio...
7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.An equatio...
7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.An equatio...
Fundamental Trig Identities  (open books to page 528 ... look at the box)
Fundamental Trig Identities           (open books to page 528 ... look at the box)Reciprocal: you already know these
Fundamental Trig Identities           (open books to page 528 ... look at the box)Reciprocal: you already know thesePythag...
Fundamental Trig Identities           (open books to page 528 ... look at the box)Reciprocal: you already know thesePythag...
Fundamental Trig Identities           (open books to page 528 ... look at the box)Reciprocal: you already know thesePythag...
Simplifying Trig Expressions
Simplifying Trig ExpressionsUse identities and other math operations to rewritea trig expression
Simplifying Trig ExpressionsUse identities and other math operations to rewritea trig expressionWe use this technique a lo...
Simplify   (1+ sinθ )(secθ − tanθ )
Simplify         (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine
Simplify         (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine                       ...
Simplify         (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine                       ...
Simplify         (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine                       ...
Simplify         (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine                       ...
Simplify         (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine                       ...
Simplify   1− cos x    sin x            +    sin x     1− cos x
Simplify       1− cos x    sin x                +        sin x     1− cos x1− cos x 1− cos x   sin x sin x        ⋅       ...
Simplify       1− cos x    sin x                +        sin x     1− cos x1− cos x 1− cos x   sin x sin x        ⋅       ...
Simplify       1− cos x    sin x                +        sin x     1− cos x1− cos x 1− cos x   sin x sin x        ⋅       ...
Simplify       1− cos x    sin x                +        sin x     1− cos x1− cos x 1− cos x   sin x sin x        ⋅       ...
Simplify       1− cos x    sin x                +        sin x     1− cos x1− cos x 1− cos x   sin x sin x        ⋅       ...
Simplify       1− cos x    sin x                +        sin x     1− cos x1− cos x 1− cos x   sin x sin x        ⋅       ...
Simplify   csc x cot x        −   sin x tan x
Simplify   csc x cot x        −   sin x tan x     1     cos x   sin x − sin x   sin x sin x     1     cos x
Simplify    csc x cot x         −    sin x tan x     1     cos x   sin x − sin x   sin x sin x     1     cos x     1    co...
Simplify    csc x cot x         −    sin x tan x     1− cos 2 x                        2     1     cos x     sin x   sin x...
Simplify    csc x cot x         −    sin x tan x     1− cos 2 x                        2     1     cos x     sin x   sin x...
Simplify   csc x cot x        −   sin x tan x     1− cos 2 x                       2     1     cos x    sin x   sin x − si...
For the next few days ... I’ll draw names “out of the hat”. Those people will be chosen to put ahomework problem on the bo...
HW #1For every pass I caught in a game, I caught athousand in practice.                              Don Hutson
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0701 ch 7 day 1

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  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
  • 1. Hand out Trig Identity Help Sheet for the start of this slide.\n2. Review why Even-Odd identities are true.\n3. Explain why Cofunction identities are true.\n\n
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  • Transcript of "0701 ch 7 day 1"

    1. 1. Chapter 7 Analytic TrigonometryMatthew 19:25-26When the disciples heard this, they were greatlyastonished and asked, "Who then can be saved?" Jesus looked at them and said, "With man this isimpossible, but with God all things are possible."
    2. 2. Chapter 7 Analytic TrigonometryMuch of this chapter will be new topics for you. Read your textbook! Study the examples!! Keep current with your homework!!! Matthew 19:25-26 When the disciples heard this, they were greatly astonished and asked, "Who then can be saved?"  Jesus looked at them and said, "With man this is impossible, but with God all things are possible."
    3. 3. 7.1 Trigonometric Identities
    4. 4. 7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.
    5. 5. 7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.An equation will be true for one or more, but notall, values of the variable in the domain.
    6. 6. 7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.An equation will be true for one or more, but notall, values of the variable in the domain. Equation : 4x − 3 = 5
    7. 7. 7.1 Trigonometric IdentitiesAn identity is an equation that is true for all valuesof the variable in the domain.An equation will be true for one or more, but notall, values of the variable in the domain. Equation : 4x − 3 = 5 2x + 14 Identity : x+7= 2
    8. 8. Fundamental Trig Identities (open books to page 528 ... look at the box)
    9. 9. Fundamental Trig Identities (open books to page 528 ... look at the box)Reciprocal: you already know these
    10. 10. Fundamental Trig Identities (open books to page 528 ... look at the box)Reciprocal: you already know thesePythagorean: hexagon on your Unit Circle
    11. 11. Fundamental Trig Identities (open books to page 528 ... look at the box)Reciprocal: you already know thesePythagorean: hexagon on your Unit CircleEven-Odd: on your help sheet
    12. 12. Fundamental Trig Identities (open books to page 528 ... look at the box)Reciprocal: you already know thesePythagorean: hexagon on your Unit CircleEven-Odd: on your help sheetCofunction: on your help sheet
    13. 13. Simplifying Trig Expressions
    14. 14. Simplifying Trig ExpressionsUse identities and other math operations to rewritea trig expression
    15. 15. Simplifying Trig ExpressionsUse identities and other math operations to rewritea trig expressionWe use this technique a lot when proving trigidentities
    16. 16. Simplify (1+ sinθ )(secθ − tanθ )
    17. 17. Simplify (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine
    18. 18. Simplify (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine ⎛ 1 sin θ ⎞ (1+ sinθ ) ⎜ − ⎝ cosθ cosθ ⎟⎠
    19. 19. Simplify (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine ⎛ 1 sin θ ⎞ (1+ sinθ ) ⎜ − ⎝ cosθ cosθ ⎟⎠ ⎛ 1− sin θ ⎞ (1+ sinθ ) ⎜ ⎝ cosθ ⎠ ⎟
    20. 20. Simplify (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine ⎛ 1 sin θ ⎞ (1+ sinθ ) ⎜ − ⎝ cosθ cosθ ⎟⎠ ⎛ 1− sin θ ⎞ (1+ sinθ ) ⎜ ⎝ cosθ ⎠ ⎟ 2 1− sin θ cosθ
    21. 21. Simplify (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine ⎛ 1 sin θ ⎞ (1+ sinθ ) ⎜ − ⎝ cosθ cosθ ⎟⎠ ⎛ 1− sin θ ⎞ (1+ sinθ ) ⎜ ⎝ cosθ ⎠ ⎟ 2 1− sin θ cosθ 2 cos θ cosθ
    22. 22. Simplify (1+ sinθ )(secθ − tanθ )a good tactic is to rewrite everything using sine & cosine ⎛ 1 sin θ ⎞ (1+ sinθ ) ⎜ − ⎝ cosθ cosθ ⎟⎠ ⎛ 1− sin θ ⎞ (1+ sinθ ) ⎜ ⎝ cosθ ⎠ ⎟ 2 1− sin θ cosθ 2 cos θ cosθ cosθ
    23. 23. Simplify 1− cos x sin x + sin x 1− cos x
    24. 24. Simplify 1− cos x sin x + sin x 1− cos x1− cos x 1− cos x sin x sin x ⋅ + ⋅ sin x 1− cos x 1− cos x sin x
    25. 25. Simplify 1− cos x sin x + sin x 1− cos x1− cos x 1− cos x sin x sin x ⋅ + ⋅ sin x 1− cos x 1− cos x sin x 2 2 (1− cos x ) + sin x sin x (1− cos x )
    26. 26. Simplify 1− cos x sin x + sin x 1− cos x1− cos x 1− cos x sin x sin x ⋅ + ⋅ sin x 1− cos x 1− cos x sin x 2 2 (1− cos x ) + sin x sin x (1− cos x ) 1− 2 cos x + cos 2 x + sin 2 x sin x (1− cos x )
    27. 27. Simplify 1− cos x sin x + sin x 1− cos x1− cos x 1− cos x sin x sin x ⋅ + ⋅ sin x 1− cos x 1− cos x sin x 2 2 (1− cos x ) + sin x sin x (1− cos x ) 1− 2 cos x + cos 2 x + sin 2 x sin x (1− cos x ) 2 − 2 cos x sin x (1− cos x )
    28. 28. Simplify 1− cos x sin x + sin x 1− cos x1− cos x 1− cos x sin x sin x ⋅ + ⋅ sin x 1− cos x 1− cos x sin x 2 (1− cos x ) + sin x2 2 (1− cos x ) sin x (1− cos x ) sin x (1− cos x ) 1− 2 cos x + cos 2 x + sin 2 x sin x (1− cos x ) 2 − 2 cos x sin x (1− cos x )
    29. 29. Simplify 1− cos x sin x + sin x 1− cos x1− cos x 1− cos x sin x sin x ⋅ + ⋅ sin x 1− cos x 1− cos x sin x 2 (1− cos x ) + sin x2 2 (1− cos x ) sin x (1− cos x ) sin x (1− cos x ) 1− 2 cos x + cos 2 x + sin 2 x 2 csc x sin x (1− cos x ) 2 − 2 cos x sin x (1− cos x )
    30. 30. Simplify csc x cot x − sin x tan x
    31. 31. Simplify csc x cot x − sin x tan x 1 cos x sin x − sin x sin x sin x 1 cos x
    32. 32. Simplify csc x cot x − sin x tan x 1 cos x sin x − sin x sin x sin x 1 cos x 1 cos 2 x 2 − 2 sin x sin x
    33. 33. Simplify csc x cot x − sin x tan x 1− cos 2 x 2 1 cos x sin x sin x − sin x sin x sin x 1 cos x 1 cos 2 x 2 − 2 sin x sin x
    34. 34. Simplify csc x cot x − sin x tan x 1− cos 2 x 2 1 cos x sin x sin x − sin x 2 sin x sin x sin x 2 sin x 1 cos x 1 cos 2 x 2 − 2 sin x sin x
    35. 35. Simplify csc x cot x − sin x tan x 1− cos 2 x 2 1 cos x sin x sin x − sin x 2 sin x sin x sin x 2 sin x 1 cos x 2 1 1 cos x 2 − 2 sin x sin x
    36. 36. For the next few days ... I’ll draw names “out of the hat”. Those people will be chosen to put ahomework problem on the board. When I draw a name, it will be for a particular problem ...
    37. 37. HW #1For every pass I caught in a game, I caught athousand in practice. Don Hutson
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