-
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...
- is multivalued:
arcsin ( 0 ) = 0 {\displaystyle \
arcsin(0)=0} , but also
arcsin ( 0 ) = π {\displaystyle \
arcsin(0)=\pi } ,
arcsin ( 0 ) = 2 π {\displaystyle...
- ) = 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...
- is: θ = 2
arcsin b 2 a = 2
arcsin 1 2 φ = 2
arcsin 5 − 1 4 = π 5 rad = 36 ∘ . {\displaystyle \theta =2\
arcsin {b \over 2a}=2\
arcsin {1 \over 2\varphi...
- functions. ∫
arcsin ( x ) d x = x
arcsin ( x ) + 1 − x 2 + C {\displaystyle \int \
arcsin(x)\,dx=x\
arcsin(x)+{\sqrt {1-x^{2}}}+C} ∫
arcsin ( a x ) d...
-
archav ( hav θ ) = 2 r
arcsin ( hav θ ) {\displaystyle d=r\operatorname {archav} (\operatorname {hav} \theta )=2r\
arcsin \left({\sqrt {\operatorname...
- 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)...
- 2 = θ 0 +
arcsin ( n sin [ α −
arcsin ( 1 n sin θ 0 ) ] ) − α {\displaystyle \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{
arcsin}}{\Big (}n\...
-
differentiating the
identity arcsin x +
arccos x = π / 2 {\displaystyle \
arcsin x+\arccos x=\pi /2} so that (
arccos x ) ′ = − (
arcsin x ) ′ {\displaystyle...
