The document discusses various mathematical concepts including trigonometric functions such as sine, cosine, and tangent. It covers trigonometric identities involving addition and subtraction formulas. It also discusses exponential functions, complex exponentials, and their relationship to trigonometric functions. Further, it briefly mentions applications of mathematics including GPS and Pokémon GO.

1. OGATA Tetsuji (@xtetsuji)
2016/09/14 Gaiax
https://flic.kr/p/9R7KgP

2. • / / OGATA Tetsuji
• @xtetsuji
• Blog: http://post.tetsuji.jp/
• RND

3. • DevOps PaaS
• OS
•
•

4. Traditional Infra Engineer

5. Traditional Infra Engineer
•
• Linux
• OS
•

6. It is Japanese traditional
•
What is this?
Japanese traditional

7. Japanese traditional

10. http://togetter.com/li/1018122

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12. http://post.tetsuji.jp/2016/08/question-what-is-math-useful/

14. 2

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• 1

21. •
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2 OK
a
sin A
=
b
sin B
=
c
sin C
= 2R
c2
= a2
+ b2
2ab cos C

22. •
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•
•
sin( ✓) = sin ✓
cos( ✓) = cos ✓
tan ✓ =
sin ✓
cos ✓
cos2
✓ + sin2
✓ = 1

23. •
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•
•
sin ✓ = x () arcsin x = ✓
cos ✓ = x () arccos x = ✓

24. …

26. •
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•
sin(↵ ± ) = sin ↵ cos ± cos ↵ sin
cos(↵ ± ) = cos ↵ cos ⌥ sin ↵ sin

31. • 1999
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32. •

34. •
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2

35. •
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37. •
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cos(a ± b) = cos a cos b ⌥ sin a sin b
sin(a ± b) = sin a cos b ± cos a sin b

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42. •
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43. z = cos ↵ + i sin ↵
w = cos + i sin
wz = (cos ↵ + i sin ↵)(cos + i sin )
= cos(↵ + ) + i sin(↵ + )

44. T =
✓
cos sin
sin cos
◆
z =
✓
cos ↵
sin ↵
◆
Tz =
✓
cos ↵ cos sin ↵ sin
sin ↵ cos + cos ↵ sin
◆
=
✓
cos(↵ + )
sin(↵ + )
◆

45. •

47. •
•
•
• x
•
eix
= cos x + i sin x

48. • sin cos
•
•
•
cos x =
eix
+ e ix
2
sin x =
eix
e ix
2i
cos(↵ + ), sin(↵ + )

49. •
• 1
•

50. • sin, cos n
• sin, cos n
• sin 1
lim
h!0
sin(x + h) sin x
h

51. lim
h!0
sin(x + h) sin x
h

53. • 1 sin(x + h)
•
•

56. •
•
• sin(x)f 1
(x)f(x) =
Z x
0
dt
p
1 t2

58. •
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59. …

60. •
• sin(x)
•
• …

61. • e^ix

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65. •
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• GPS Pokémon GO

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68. • TIE = Traditional Infra Engineer
•