Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
trigonometric function |
| gptkbp:appearsIn |
gptkb:polar_coordinates
Fourier analysis computer graphics partial differential equations vector calculus complex numbers mathematical modeling analytic geometry wave equations oscillatory motion right triangle circular functions hyperbolic functions |
| gptkbp:complex_extension |
tan(z) = sin(z)/cos(z) for complex z
|
| gptkbp:defines |
tan(x) = sin(x)/cos(x)
|
| gptkbp:domain |
all real numbers except odd multiples of π/2
|
| gptkbp:even/odd |
odd
|
| gptkbp:first_derivative |
sec^2(x)
|
| gptkbp:graphics |
repeats every π, has vertical asymptotes at x = (2n+1)π/2
|
| https://www.w3.org/2000/01/rdf-schema#label |
Tangent (mathematics)
|
| gptkbp:integration |
-ln|cos(x)| + C
|
| gptkbp:inverse_function |
arctangent
|
| gptkbp:notableDerivative |
sec^2(x)
|
| gptkbp:notation |
tan(x)
|
| gptkbp:odd_function |
true
|
| gptkbp:range |
all real numbers
|
| gptkbp:reciprocal |
cotangent
|
| gptkbp:recurrence |
π
|
| gptkbp:relatedTo |
cosine
sine cotangent secant |
| gptkbp:right_triangle_definition |
opposite/adjacent
|
| gptkbp:second_derivative |
2 tan(x) sec^2(x)
|
| gptkbp:symbol |
tan
|
| gptkbp:Taylor_series_at_x=0 |
x + x^3/3 + 2x^5/15 + 17x^7/315 + ...
|
| gptkbp:undefined_at |
x = (2n+1)π/2, n ∈ ℤ
|
| gptkbp:used_in |
gptkb:geometry
gptkb:navigation gptkb:signal_processing calculus complex analysis engineering physics trigonometry |
| gptkbp:bfsParent |
gptkb:TAN
|
| gptkbp:bfsLayer |
6
|