-
convention is to name
inverse trigonometric functions using an arc- prefix:
arcsin(x), arccos(x), arctan(x), etc. (This
convention is used
throughout this...
-
arcsin x ) {\displaystyle \cot(\
arcsin x)} is: cot (
arcsin x ) = 1 tan (
arcsin x ) = 1 x 1 − x 2 = 1 − x 2 x {\displaystyle \cot(\
arcsin x)={\frac...
- It
follows that the
arcsine function is multivalued:
arcsin(0) = 0, but also
arcsin(0) = π,
arcsin(0) = 2π, etc. When only one
value is desired, the function...
- h ) = 2 r
arcsin ( h ) {\displaystyle d=r\operatorname {archav} (h)=2r\
arcsin \left({\sqrt {h}}\right)} or more explicitly: d = 2 r
arcsin ( hav ...
- ) = 2 π
arcsin ( x ) =
arcsin ( 2 x − 1 ) π + 1 2 {\displaystyle F(x)={\frac {2}{\pi }}\
arcsin \left({\sqrt {x}}\right)={\frac {\
arcsin(2x-1)}{\pi...
- x = a cos θ d θ , θ =
arcsin x a . {\displaystyle x=a\sin \theta ,\quad dx=a\cos \theta \,d\theta ,\quad \theta =\
arcsin {\frac {x}{a}}.} Then, ∫...
- arcsine-distributed if Pr [ X ≤ x ] = 2 π
arcsin ( x ) , ∀ x ∈ [ 0 , 1 ] . {\displaystyle \Pr \left[X\leq x\right]={\frac {2}{\pi }}\
arcsin \left({\sqrt {x}}\right)...
-
following modified formula[citation needed] δ = 2
arcsin ( d a c t 2 D ) {\displaystyle \delta =2\
arcsin \left({\frac {d_{\mathrm {act} }}{2D}}\right)}...
- \lambda ,\cos \lambda )} and declination, δ =
arcsin ( sin ϵ sin λ ) {\displaystyle \delta =\
arcsin(\sin \epsilon \sin \lambda )} . Right-handed...
-
differentiating the
identity arcsin x +
arccos x = π / 2 {\displaystyle \
arcsin x+\arccos x=\pi /2} so that (
arccos x ) ′ = − (
arcsin x ) ′ {\displaystyle...
