|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:addition_formula
|
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
|
|
gptkbp:amplitude
|
1
|
|
gptkbp:antiderivative
|
-Cosine function
|
|
gptkbp:codomain
|
[-1, 1]
|
|
gptkbp:differential_equation
|
y'' + y = 0
|
|
gptkbp:domain
|
Real numbers
|
|
gptkbp:Euler's_formula
|
sin(x) = (e^{ix} - e^{-ix})/(2i)
|
|
gptkbp:evenOrOdd
|
Odd function
|
|
gptkbp:first_maximum
|
π/2
|
|
gptkbp:first_minimum
|
3π/2
|
|
gptkbp:first_negative_zero
|
-π
|
|
gptkbp:first_positive_zero
|
π
|
|
gptkbp:firstAppearance
|
Ancient Greece
|
|
gptkbp:Fourier_transform
|
(π/i)[δ(ω-1)-δ(ω+1)]
|
|
gptkbp:frequency
|
1/(2π)
|
|
gptkbp:graphics
|
wind
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Sine function
|
|
gptkbp:integral_over_period
|
0
|
|
gptkbp:inverse_function
|
Arcsine function
|
|
gptkbp:is_solution_of
|
gptkb:Simple_harmonic_oscillator
|
|
gptkbp:is_used_to_model
|
gptkb:music
gptkb:Waves
Light
Oscillations
|
|
gptkbp:Laplace_transform
|
s/(s^2 + ω^2)
|
|
gptkbp:maximumCategory
|
1
|
|
gptkbp:minimum_value
|
-1
|
|
gptkbp:multiplication_formula
|
sin(a)sin(b) = 1/2[cos(a-b) - cos(a+b)]
|
|
gptkbp:notableDerivative
|
gptkb:Cosine_function
|
|
gptkbp:period
|
2π
|
|
gptkbp:phase_shift
|
0
|
|
gptkbp:recurrence
|
sin(x+π) = -sin(x)
|
|
gptkbp:relatedTo
|
gptkb:Cosine_function
Cosecant function
Tangent function
|
|
gptkbp:symbol
|
sin(x)
|
|
gptkbp:symmetry
|
Origin
|
|
gptkbp:Taylor_series_at_0
|
x - x^3/3! + x^5/5! - x^7/7! + ...
|
|
gptkbp:unit_circle_definition
|
y-coordinate of point at angle x
|
|
gptkbp:used_in
|
gptkb:Physics
gptkb:Calculus
gptkb:Trigonometry
Engineering
|
|
gptkbp:value_at_0
|
0
|
|
gptkbp:value_at_2π
|
0
|
|
gptkbp:value_at_3π/2
|
-1
|
|
gptkbp:value_at_π
|
0
|
|
gptkbp:value_at_π/2
|
1
|
|
gptkbp:zeroes
|
nπ, n ∈ ℤ
|
|
gptkbp:bfsParent
|
gptkb:Unit_circle
gptkb:Entire_Functions
|
|
gptkbp:bfsLayer
|
7
|