-
inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x),
arctan(x), etc. (This
convention is used
throughout this article.) This notation...
-
arctan 1 2 +
arctan 1 3 , {\displaystyle {\frac {\pi }{4}}=\
arctan {\frac {1}{2}}+\
arctan {\frac {1}{3}},} π =
arctan 1 +
arctan 2 +
arctan ...
- Gregory's series, is
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...
- sgn ( y )
arccos x x 2 + y 2 = {
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...
-
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 ...
- 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...
- x ) =
arctan ( y / x ) . {\textstyle \theta =\operatorname {atan2} (y,x)=\
arctan \left(y/x\right).} However, when x < 0, the
angle arctan ( y /...
-
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...
- 4 = 2
arctan 1 3 +
arctan 1 7 {\displaystyle {\frac {\pi }{4}}=2\
arctan {\frac {1}{3}}+\
arctan {\frac {1}{7}}} π 4 = 4
arctan 1 5 −
arctan 1 239...
-
Therefore also 4
arctan 1 5 − π 4 = 4
arctan 1 5 −
arctan 1 1 = 4
arctan 1 5 +
arctan − 1 1 =
arctan 120 119 +
arctan − 1 1 =
arctan 120 ⋅ 1...
