- 5em]\operatorname {
arccsc}(x)&={\frac {\pi }{2}}-\operatorname {arcsec}(x)\end{aligned}}}
Negative arguments: arcsin(−x)=−arcsin(x)
arccsc(−x)=−
arccsc...
- x)&=x\\\sin(\operatorname {
arccsc} x)&={\frac {1}{x}}&\cos(\operatorname {
arccsc} x)&={\frac {\sqrt {x^{2}-1}}{x}}&\tan(\operatorname {
arccsc} x)&={\frac {1}{\sqrt...
- -1)} ∫
arccsc(x)dx=xarccsc(x)+ln(|x|+x2−1)+C=xarccsc(x)+arcosh|x|+C{\displaystyle \int \operatorname {
arccsc}(x)\,dx=x\operatorname {
arccsc}(x)\,+\...
- {1}{|x|{\sqrt {x^{2}-1}}}}} Let y=arccscx ∣|x|≥1{\displaystyle y=\operatorname {
arccsc} x\ \mid |x|\geq 1} Then x=cscy ∣ y∈[−π2,0)∪(0,π2]{\displaystyle x=\csc...
-
arccosec –
inverse cosecant function. (Also
written as
arccsc.)
arccot –
inverse cotangent function.
arccsc –
inverse cosecant function. (Also
written as arccosec...
- \pi ,\;y\neq {\frac {\pi }{2}}} y=arccscx{\displaystyle y=\operatorname {
arccsc} x} cscy=x{\displaystyle \csc y=x} x<−1 or x>1{\displaystyle x<-1{\text{...
- 1 to
infinity the
orbit is a
hyperbola branch making a
total turn of 2
arccsc(e),
decreasing from 180 to 0 degrees. Here, the
total turn is analogous...
- ≤ y < π/2 or π/2 < y ≤ π 0° ≤ y < 90° or 90° < y ≤ 180°
arccosecant y =
arccsc(x) x = csc(y) x ≤ −1 or 1 ≤ x −π/2 ≤ y < 0 or 0 < y ≤ π/2 −90° ≤ y < 0°...
- for |x|≥1{\displaystyle \int \operatorname {
arccsc} {x}\,dx=x\operatorname {
arccsc} {x}+\ln \left\vert x\,\left(1+{\sqrt {1-x^{-2}}}\,\right)\right\vert...
- {\frac {d}{dx}}\csc x=-\csc {x}\cot {x}} ddxarccscx=−1|x|x2−1{\displaystyle {\frac {d}{dx}}\operatorname {
arccsc} x=-{\frac {1}{|x|{\sqrt {x^{2}-1}}}}}...
