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inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x),
arctan(x), etc. (This
convention is used
throughout this article.) This notation...
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arctan 1 2 +
arctan 1 3 , {\displaystyle {\frac {\pi }{4}}=\
arctan {\frac {1}{2}}+\
arctan {\frac {1}{3}},} π =
arctan 1 +
arctan 2 +
arctan ...
- x ) =
arctan ( y / x ) . {\textstyle \theta =\operatorname {atan2} (y,x)=\
arctan \left(y/x\right).} However, when x < 0, the
angle arctan ( y /...
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arctangent function:
arctan x = x − x 3 3 + x 5 5 − x 7 7 + ⋯ = ∑ k = 0 ∞ ( − 1 ) k x 2 k + 1 2 k + 1 . {\displaystyle \
arctan x=x-{\frac {x^{3}}{3}}+{\frac...
- 4 = 6
arctan 1 8 + 2
arctan 1 57 +
arctan 1 239 {\displaystyle {\frac {\pi }{4}}=6\
arctan {\frac {1}{8}}+2\
arctan {\frac {1}{57}}+\
arctan {\frac...
- 0 π 2 y | y | if x = 0 and y ≠ 0
arctan ( y x ) if x > 0
arctan ( y x ) + π if x < 0 and y ≥ 0
arctan ( y x ) − π if x < 0 and y < 0 {\displaystyle...
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function f ( x ) =
arctan x {\displaystyle f(x)=\
arctan x}
Gudermannian function f ( x ) = gd ( x ) = ∫ 0 x d t cosh t = 2
arctan ( tanh ( x 2...
- horizontally, α h = 2
arctan h 2 f = 2
arctan 36 2 × 50 ≈ 39.6 ∘ {\displaystyle \alpha _{h}=2\
arctan {\frac {h}{2f}}=2\
arctan {\frac {36}{2\times 50}}\approx...
- with
respect to the base line, i.e. ϕ ( t ) =
arctan ( Δ Y t Δ X t ) . {\displaystyle \phi (t)=\
arctan \left({\frac {\Delta Yt}{\Delta Xt}}\right).}...
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arctan s +
arctan t =
arctan s + t 1 − s t {\displaystyle \
arctan s+\
arctan t=\
arctan {\frac {s+t}{1-st}}} holds,
provided arctan s +
arctan ...
