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Calculus 2 > Trig / Hyperbolic Functions / Physical App Equations > Flashcards

Trig / Hyperbolic Functions / Physical App Equations Flashcards

1
Q

tan(θ) =

A

sinθ/cosθ

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2
Q

cot(θ) =

A

cos(θ)/sin(θ)

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3
Q

? + cos²(θ) = 1

A

sin²(θ)

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4
Q

sec²(θ) - ? = 1

A

tan²(θ)

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5
Q

csc²(θ) - ? = 1

A

cot²(θ)

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6
Q

1/sin(θ) =

A

csc(θ)

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7
Q

1/cos(θ) =

A

sec(θ)

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8
Q

sin(α+β) =

A

sin(α)cos(β) + cos(α)sin(β)

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9
Q

sin(α-β) =

A

sin(α)cos(β) - cos(α)sin(β)

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10
Q

cos(α+β) =

A

cos(α)cos(β) - sin(α)sin(β)

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11
Q

cos(α-β) =

A

cos(α)cos(β) + sin(α)sin(β)

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12
Q

sin(2*θ) =

A

2sin(θ)cos(θ)

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13
Q

cos(2*θ) =

A

All the same:
cos²(θ)-sin²(θ) OR
2cos²(θ) - 1 OR
1 - 2sin²(θ)

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14
Q

cos²(θ) =

A

(1+cos(2*θ))/2

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15
Q

sin²(θ) =

A

(1-cos(2*θ))/2

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16
Q

tan²(θ) =

A

(1-cos(2θ))/(1+cos(2θ))

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17
Q

cos(0) =

A

1

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18
Q

cos(180) =

A

-1

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19
Q

cos(90) AND cos(-90) =

A

0

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20
Q

sin(0) OR sin(180) =

A

0

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21
Q

sin(90) =

A

1

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22
Q

sin(270) =

A

-1

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23
Q

derive: sin(x)

A

cos(x)

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24
Q

derive: cos(x)

A

-sin(x)

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25
Q

derive: tan(x)

A

sec²(x)

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26
Q

derive: sec(x)

A

sec(x) * tan(x)

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27
Q

derive: csc(x)

A

-csc(x) * cot(x)

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28
Q

derive: cot(x)

A

-csc²(x)

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29
Q

derive: sin^-1(x)

A

1 / √(1-x²)

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30
Q

derive: cos^-1(x)

A

-1 / √(1-x²)

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31
Q

derive: tan^-1(x)

A

1 / (1+x²)

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32
Q

integrate: cos(x)

A

sin(x)

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33
Q

integrate: sin(x)

A

-cos(x)

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34
Q

integrate: sec²(x)

A

tan(x)

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35
Q

integrate: sec(x)*tan(x)

A

sec(x)

36
Q

integrate: csc(x) * cot(x)

A

-csc(x)

37
Q

integrate: csc²(x)

A

-cot(x)

38
Q

integrate: tan(x)

A

ln( [abs value of] sec(x) )

39
Q

integrate: sec(x)

A

ln( [abs value of] sec(x) + tan(x))

40
Q

tan(0) AND tan(180) =

A

0

41
Q

sinh(x) =

A

(e^x - e^(-x))/2

42
Q

cosh(x) =

A

(e^x + e^(-x))/2

43
Q

sech(x) =

A

1/cosh(x) OR
2/(e^x + e^(-x))

44
Q

csch(x) =

A

1/sinh(x) OR
2/(e^x - e^(-x))

45
Q

tanh(x) =

A

sinh(x) / cosh(x) OR
(e^x - e^(-x)) / (e^x + e^(-x))

46
Q

coth(x) =

A

1/tanh(x) OR
cosh(x)/sinh(x) OR
(e^x+e^(-x)) / (e^x - e^(-x))

47
Q

cosh²(x) - ? = 1

A

sinh²(x)

48
Q

tanh² + ? = 1

A

sech²(x)

49
Q

coth²(x) - ? = 1

A

csch²(x)

50
Q

sinh(x + y) =

A

sinh(x)cosh(y) + cosh(x)sinh(y)

51
Q

sinh(x - y) =

A

sinh(x)cosh(y) - cosh(x)sinh(y)

52
Q

cosh(x + y)

A

cosh(x)cosh(y) + sinh(x)sinh(y)

53
Q

cosh(x - y)

A

cosh(x)cosh(y) - sinh(x)sinh(y)

54
Q

sinh²(x) =

A

(-1 + cosh(2*x))/2

55
Q

sinh(2*x) =

A

2sinh(x)cosh(x)

56
Q

cosh²(x) =

A

(1 + cosh(2*x))/2

57
Q

cosh(2*x) =

A

cosh²(x) + sinh²(x)

58
Q

sinh(0) =

A

0

59
Q

cosh(0) =

A

1

60
Q

tanh(0) =

A

0

61
Q

tanh(2x) =

A

2*tanh(x) / (1+tanh²(x))

62
Q

coth(x) - tanh(x) =

A

2csch(2x)

63
Q

coth(x) + tanh(x) =

A

2coth(2x)

64
Q

derive: sinh(x)

A

cosh(x)

65
Q

derive: cosh(x)

A

sinh(x)

66
Q

derive: tanh(x)

A

sech²(x)

67
Q

derive: coth(x)

A

-csch²(x)

68
Q

derive: sech(x)

A

-sech(x) * tanh(x)

69
Q

derive: csch(x)

A

-csch(x) * coth(x)

70
Q

integrate: cosh(x)

A

sinh(x)

71
Q

integrate: sinh(x)

A

cosh(x)

72
Q

integrate: sech²(x)

A

tanh(x)

73
Q

integrate: csch²(x)

A

-coth(x)

74
Q

integrate: sech(x) * tanh(x)

A

-sech(x)

75
Q

integrate: csch(x) * coth(x)

A

-csch(x)

76
Q

integrate: tanh(x)

A

ln(cosh(x))

77
Q

integrate: coth(x)

A

ln([abs value of] sinh(x))

78
Q

integrate: sech(x)

A

tan^-1 (sinh(x))

79
Q

integrate: csch(x)

A

ln([abs value of] tanh(x/2))

80
Q

ln(1) =

A

0

81
Q

integrate: ln(b*x)

A

xln(bx) - x

82
Q

Force = ?

A

mass * acceleration

83
Q

Work =

A

The Integral of FORCE

84
Q

Force [Springs] =

A

k*x

85
Q

Volume =

A

area * thickness

86
Q

mass =

A

Volume * Density OR
Weight/Gravity

Calculus 2 (1 decks)

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