-
inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x),
arctan(x), etc. (This
convention is used
throughout this article.) This notation...
- x ) =
arctan ( y / x ) . {\textstyle \theta =\operatorname {atan2} (y,x)=\
arctan \left(y/x\right).} However, when x < 0, the
angle arctan ( y /...
- 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...
- formula: π 4 = 4
arctan ( 1 5 ) −
arctan ( 1 70 ) +
arctan ( 1 99 ) {\displaystyle {\pi \over 4}=4\
arctan \left({1 \over 5}\right)-\
arctan \left({1 \over...
-
arctan 1 2 +
arctan 1 3 , {\displaystyle {\frac {\pi }{4}}=\
arctan {\frac {1}{2}}+\
arctan {\frac {1}{3}},} π =
arctan 1 +
arctan 2 +
arctan ...
- the
focal point: a = 2
arctan ( D / 2 f ) = 2
arctan ( D 2 f ) {\displaystyle a=2\
arctan \left({\frac {D/2}{f}}\right)=2\
arctan \left({\frac {D}{2f}}\right)}...
-
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...
- 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...
-
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...
-
converged much faster: π 4 = 4
arctan 1 5 −
arctan 1 239 . {\displaystyle {\frac {\pi }{4}}=4\
arctan {\frac {1}{5}}-\
arctan {\frac {1}{239}}.}
Machin reached...
