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gptkbp:instanceOf
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Mathematical Function
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gptkbp:amplitude
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1
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gptkbp:analytic
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Yes
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gptkbp:category
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gptkb:Trigonometric_Function
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gptkbp:codomain
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[-1, 1]
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gptkbp:continuity
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Yes
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gptkbp:differentiable
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Yes
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gptkbp:differential_equation
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y'' + y = 0
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gptkbp:domain
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All real numbers
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gptkbp:Euler's_formula
|
sin(x) = (e^{ix} - e^{-ix})/(2i)
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gptkbp:evenOrOdd
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Odd function
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gptkbp:firstAppearance
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gptkb:Ancient_India
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gptkbp:Fourier_transform
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Related to Dirac delta functions
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gptkbp:frequency
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1/(2π)
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gptkbp:fundamental_identity
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sin^2(x) + cos^2(x) = 1
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gptkbp:graphics
|
Smooth, periodic wave
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https://www.w3.org/2000/01/rdf-schema#label
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Sine Function
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gptkbp:integration
|
-cos(x) + C
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gptkbp:inverse_function
|
arcsin(x)
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gptkbp:Laplace_transform
|
1/(s^2 + 1)
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gptkbp:maximumCategory
|
1
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gptkbp:minimum_value
|
-1
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gptkbp:notableDerivative
|
cos(x)
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gptkbp:notation
|
single
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gptkbp:orthogonal_to
|
gptkb:Cosine_Function
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gptkbp:orthonormal_basis
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Yes, in L2[0,2π]
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gptkbp:par
|
Odd
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gptkbp:period
|
2π
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gptkbp:range
|
[-1, 1]
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gptkbp:relatedTo
|
gptkb:Cosecant_Function
gptkb:Tangent_Function
gptkb:Cosine_Function
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gptkbp:roots
|
nπ, n ∈ ℤ
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gptkbp:symbol
|
sin(x)
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gptkbp:Taylor_series_at_0
|
x - x^3/3! + x^5/5! - x^7/7! + ...
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gptkbp:unit_circle_definition
|
y-coordinate of point at angle x
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gptkbp:used_in
|
gptkb:Signal_Processing
gptkb:Physics
gptkb:Harmonic_Motion
gptkb:Wave_Equations
gptkb:Trigonometry
gptkb:Fourier_Series
Engineering
|
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gptkbp:value_at_0
|
0
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gptkbp:value_at_2π
|
0
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gptkbp:value_at_3π/2
|
-1
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gptkbp:value_at_π
|
0
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gptkbp:value_at_π/2
|
1
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gptkbp:zeroes
|
nπ, n ∈ ℤ
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gptkbp:bfsParent
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gptkb:Analytic_Functions
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gptkbp:bfsLayer
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6
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