Term
Double-Angle Identity
sin(2X) |
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Definition
Double-Angle Identity
2sin(x)cos(x) |
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Term
Double-Angle Identities
cos(2x) |
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Definition
Double-Angle Identities
cos2(x)-sin2(x)
2cos2(x)-1
1-2sin2(x) |
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Term
Double-Angle Identities
tan(2x) |
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Definition
Double-Angle Identities
2tan(x)
1-tan2(x) |
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Term
Half-Angle Identities
sin2(x) |
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Definition
Half Angle Identities
1/2 (1-cos(2x)) |
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Term
Half-Angle Identities
cos2(x) |
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Definition
Half-Angle Identities
1/2 (1+cos(2x)) |
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Term
Addition Identities
sin(a+b)
sin(a-b) |
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Definition
Addition Identities
sin(a)cos(b) + sin(b)cos(a)
sin(a)cos(b) - sin(b)cos(a) |
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Term
Addition Identities
cos(a+b)
cos(a-b)
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Definition
Addition Identities
cos(a)cos(b) - sin(a)sin(b)
cos(a)cos(b) + sin(a)sin(b)
(signs are opposite) |
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Term
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Definition
Trig Integrals
ln|sec(x)| + C |
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Term
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Definition
Trig Integrals
ln|sec(x) + tan(x)| |
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Term
Trig Identities
Pythagorean Identities |
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Definition
Trig Identities
sin2(x) + cos2(x) = 1
sec2(x) - 1 = tan2(x)
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Term
Error Bounds
Simpson's Rule |
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Definition
Error Bound
|Sn| ≤ M(b - a)5
180n4
when |f4(x)| ≤ M on [a,b] |
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Term
Error Bound
Trapezoid Rule |
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Definition
Error Bound
|Tn| ≤ M(b-a)3
12 n2
when M ≥ |f "(x)| on [a,b] |
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Term
Error Bound
Taylor Polynomials |
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Definition
Error Bound
|Rn(x)| ≤ M |x-a|(n+1)
(n+1)!
when |f (n+1)(x)| ≤ M |
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Term
Taylor Series
General Formula |
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Definition
Taylor Series
Tn = Σ f (n)(a)(x-a)n
n! |
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Term
Taylor Series
Series Representation of ex |
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Definition
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Term
Taylor Series
Series representation of cos(x) |
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Definition
Taylor Series
∑(-1)n(x)2n
(2n)! |
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Term
MacLaurin Series
General Form |
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Definition
MacLaurin Series
∑f n(0)xn
n! |
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Term
Geometric Series
General form and solution |
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Definition
Geometric Series
∑xn = 1/(1-x)
∑arn = a/(1-r) |
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