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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:trigonometric_function
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gptkbp:appearsIn
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gptkb:computer_graphics
gptkb:partial_differential_equations
gptkb:polar_coordinates
Fourier analysis
vector calculus
complex numbers
mathematical modeling
analytic geometry
wave equations
oscillatory motion
right triangle
circular functions
hyperbolic functions
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gptkbp:complex_extension
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tan(z) = sin(z)/cos(z) for complex z
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gptkbp:defines
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tan(x) = sin(x)/cos(x)
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gptkbp:domain
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all real numbers except odd multiples of π/2
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gptkbp:even/odd
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odd
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gptkbp:first_derivative
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sec^2(x)
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gptkbp:graphics
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repeats every π, has vertical asymptotes at x = (2n+1)π/2
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gptkbp:integration
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-ln|cos(x)| + C
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gptkbp:inverse_function
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arctangent
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gptkbp:notableDerivative
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sec^2(x)
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gptkbp:notation
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tan(x)
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gptkbp:odd_function
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true
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gptkbp:range
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all real numbers
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gptkbp:reciprocal
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cotangent
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gptkbp:recurrence
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π
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gptkbp:relatedTo
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cosine
sine
cotangent
secant
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gptkbp:right_triangle_definition
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opposite/adjacent
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gptkbp:second_derivative
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2 tan(x) sec^2(x)
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gptkbp:symbol
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tan
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gptkbp:Taylor_series_at_x=0
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x + x^3/3 + 2x^5/15 + 17x^7/315 + ...
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gptkbp:undefined_at
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x = (2n+1)π/2, n ∈ ℤ
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gptkbp:used_in
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gptkb:geometry
gptkb:navigation
gptkb:signal_processing
calculus
complex analysis
engineering
physics
trigonometry
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gptkbp:bfsParent
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gptkb:TAN
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gptkbp:bfsLayer
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7
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https://www.w3.org/2000/01/rdf-schema#label
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Tangent (mathematics)
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