Trig / Hyperbolic Functions / Physical App Equations Flashcards
1
Q
tan(θ) =
A
sinθ/cosθ
2
Q
cot(θ) =
A
cos(θ)/sin(θ)
3
Q
? + cos²(θ) = 1
A
sin²(θ)
4
Q
sec²(θ) - ? = 1
A
tan²(θ)
5
Q
csc²(θ) - ? = 1
A
cot²(θ)
6
Q
1/sin(θ) =
A
csc(θ)
7
Q
1/cos(θ) =
A
sec(θ)
8
Q
sin(α+β) =
A
sin(α)cos(β) + cos(α)sin(β)
9
Q
sin(α-β) =
A
sin(α)cos(β) - cos(α)sin(β)
10
Q
cos(α+β) =
A
cos(α)cos(β) - sin(α)sin(β)
11
Q
cos(α-β) =
A
cos(α)cos(β) + sin(α)sin(β)
12
Q
sin(2*θ) =
A
2sin(θ)cos(θ)
13
Q
cos(2*θ) =
A
All the same:
cos²(θ)-sin²(θ) OR
2cos²(θ) - 1 OR
1 - 2sin²(θ)
14
Q
cos²(θ) =
A
(1+cos(2*θ))/2
15
Q
sin²(θ) =
A
(1-cos(2*θ))/2
16
Q
tan²(θ) =
A
(1-cos(2θ))/(1+cos(2θ))
17
Q
cos(0) =
A
1
18
Q
cos(180) =
A
-1
19
Q
cos(90) AND cos(-90) =
A
0
20
Q
sin(0) OR sin(180) =
A
0
21
Q
sin(90) =
A
1
22
Q
sin(270) =
A
-1
23
Q
derive: sin(x)
A
cos(x)
24
Q
derive: cos(x)
A
-sin(x)
25
derive: tan(x)
sec²(x)
26
derive: sec(x)
sec(x) * tan(x)
27
derive: csc(x)
-csc(x) * cot(x)
28
derive: cot(x)
-csc²(x)
29
derive: sin^-1(x)
1 / √(1-x²)
30
derive: cos^-1(x)
-1 / √(1-x²)
31
derive: tan^-1(x)
1 / (1+x²)
32
integrate: cos(x)
sin(x)
33
integrate: sin(x)
-cos(x)
34
integrate: sec²(x)
tan(x)
35
integrate: sec(x)*tan(x)
sec(x)
36
integrate: csc(x) * cot(x)
-csc(x)
37
integrate: csc²(x)
-cot(x)
38
integrate: tan(x)
ln( [abs value of] sec(x) )
39
integrate: sec(x)
ln( [abs value of] sec(x) + tan(x))
40
tan(0) AND tan(180) =
0
41
sinh(x) =
(e^x - e^(-x))/2
42
cosh(x) =
(e^x + e^(-x))/2
43
sech(x) =
1/cosh(x) OR
2/(e^x + e^(-x))
44
csch(x) =
1/sinh(x) OR
2/(e^x - e^(-x))
45
tanh(x) =
sinh(x) / cosh(x) OR
(e^x - e^(-x)) / (e^x + e^(-x))
46
coth(x) =
1/tanh(x) OR
cosh(x)/sinh(x) OR
(e^x+e^(-x)) / (e^x - e^(-x))
47
cosh²(x) - ? = 1
sinh²(x)
48
tanh² + ? = 1
sech²(x)
49
coth²(x) - ? = 1
csch²(x)
50
sinh(x + y) =
sinh(x)*cosh(y) + cosh(x)*sinh(y)
51
sinh(x - y) =
sinh(x)*cosh(y) - cosh(x)*sinh(y)
52
cosh(x + y)
cosh(x)*cosh(y) + sinh(x)*sinh(y)
53
cosh(x - y)
cosh(x)*cosh(y) - sinh(x)*sinh(y)
54
sinh²(x) =
(-1 + cosh(2*x))/2
55
sinh(2*x) =
2*sinh(x)*cosh(x)
56
cosh²(x) =
(1 + cosh(2*x))/2
57
cosh(2*x) =
cosh²(x) + sinh²(x)
58
sinh(0) =
0
59
cosh(0) =
1
60
tanh(0) =
0
61
tanh(2x) =
2*tanh(x) / (1+tanh²(x))
62
coth(x) - tanh(x) =
2*csch(2*x)
63
coth(x) + tanh(x) =
2*coth(2*x)
64
derive: sinh(x)
cosh(x)
65
derive: cosh(x)
sinh(x)
66
derive: tanh(x)
sech²(x)
67
derive: coth(x)
-csch²(x)
68
derive: sech(x)
-sech(x) * tanh(x)
69
derive: csch(x)
-csch(x) * coth(x)
70
integrate: cosh(x)
sinh(x)
71
integrate: sinh(x)
cosh(x)
72
integrate: sech²(x)
tanh(x)
73
integrate: csch²(x)
-coth(x)
74
integrate: sech(x) * tanh(x)
-sech(x)
75
integrate: csch(x) * coth(x)
-csch(x)
76
integrate: tanh(x)
ln(cosh(x))
77
integrate: coth(x)
ln([abs value of] sinh(x))
78
integrate: sech(x)
tan^-1 (sinh(x))
79
integrate: csch(x)
ln([abs value of] tanh(x/2))
80
ln(1) =
0
81
integrate: ln(b*x)
x*ln(b*x) - x
82
Force = ?
mass * acceleration
83
Work =
The Integral of FORCE
84
Force [Springs] =
k*x
85
Volume =
area * thickness
86
mass =
Volume * Density OR
Weight/Gravity
