解 x
x=arcSin(y^{-1})+2\pi n_{9}\text{, }n_{9}\in \mathrm{Z}\text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(\left(n_{4}\text{bmod}2=1\text{ and }not(y>-1)\text{ and }n_{4}=\left(-1\right)\left(2+\left(-2\right)n_{9}\right)\right)\text{ or }\left(not(|y|<1)\text{ and }y>\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }n_{4}=\left(-1\right)\left(2+\left(-2\right)n_{9}\right)\right)\text{ or }\left(y>\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }not(y>-1)\text{ and }n_{4}=\left(-1\right)\left(2+\left(-2\right)n_{9}\right)\right)\text{ or }\left(n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }not(y<1)\text{ and }n_{4}=\left(-1\right)\left(2+\left(-2\right)n_{9}\right)\right)\text{ or }\left(not(|y|<1)\text{ and }y<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }n_{4}=\left(-1\right)\left(2+\left(-2\right)n_{9}\right)\right)\text{ or }\left(y<\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }not(y<1)\text{ and }n_{4}=2n_{9}\right)\text{ or }\left(n_{4}\text{bmod}2=1\text{ and }not(y<1)\text{ and }n_{4}=2n_{9}\right)\text{ or }\left(n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }y>\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\text{ and }not(y<1)\right)\text{ or }\left(y<\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }not(|y|<1)\text{ and }n_{4}=2n_{9}\right)\text{ or }\left(y<\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }not(|y|<1)\text{ and }y<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\right)\text{ or }\left(y<\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }not(|y|<1)\text{ and }y>\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\right)\text{ or }\left(y<\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\text{ and }not(y>-1)\right)\text{ or }\left(y>\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }not(|y|<1)\text{ and }n_{4}=2n_{9}\right)\text{ or }\left(y>\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }not(|y|<1)\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\text{ and }not(y=\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}})\right)\text{ or }\left(n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }not(y>-1)\text{ and }n_{4}=2n_{9}\right)\text{ or }\left(n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }not(y>-1)\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\right)\text{ or }\left(n_{4}\text{bmod}2=1\text{ and }not(n_{4}>2n_{9})\text{ and }not(y<1)\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}<\left(-1\right)\left(2+\left(-2\right)n_{9}\right))\right)\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }arcSin(y^{-1})+2\pi n_{9}=\frac{1}{2}\pi +\pi n_{1}
x=\pi +2n_{18}\pi +\left(-1\right)arcSin(y^{-1})\text{, }n_{18}\in \mathrm{Z}\text{, }\exists n_{4}\in \mathrm{Z}\text{ : }\left(\left(\left(not(y<1)\text{ and }not(n_{4}<-1+2n_{18})\text{ and }n_{4}\text{bmod}2=0\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }\exists n_{22}\in \mathrm{Z}\text{ : }n_{4}=1+\left(-2\right)n_{22}\text{ and }not(n_{4}>1+2n_{18})\right)\text{ or }\left(y<\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }not(n_{4}<-1+2n_{18})\text{ and }n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }\exists n_{22}\in \mathrm{Z}\text{ : }n_{4}=1+\left(-2\right)n_{22}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }\nexists n_{26}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{26}\right)\text{ or }\left(not(y>-1)\text{ and }\left(-1\right)n_{4}\text{bmod}2=1\text{ and }n_{4}\text{bmod}2=0\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(n_{4}<-1+2n_{18})\right)\text{ or }\left(not(y>-1)\text{ and }-1<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }not(n_{4}>1+2n_{18})\text{ and }\exists n_{22}\in \mathrm{Z}\text{ : }n_{4}=1+\left(-2\right)n_{22}\text{ and }\exists n_{26}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{26}\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}<-1+2n_{18})\right)\text{ or }\left(not(y>-1)\text{ and }not(n_{4}<-1+2n_{18})\text{ and }n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }\exists n_{26}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{26}\text{ and }\exists n_{22}\in \mathrm{Z}\text{ : }n_{4}=1+\left(-2\right)n_{22}\text{ and }not(n_{4}>1+2n_{18})\right)\text{ or }\left(not(y>-1)\text{ and }not(n_{4}<-1+2n_{18})\text{ and }n_{4}\text{bmod}2=0\text{ and }n_{4}\text{bmod}2=1\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\right)\text{ or }\left(y<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(n_{4}<-1+2n_{18})\right)\text{ or }\left(y<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}>1+2n_{18})\text{ and }\exists n_{22}\in \mathrm{Z}\text{ : }n_{4}=1+\left(-2\right)n_{22}\text{ and }\exists n_{26}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{26}\text{ and }not(n_{4}<-1+2n_{18})\right)\right)\text{ or }\left(\left(\left(\left(\left(\left(y>\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(|y|<1)\text{ and }y>\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}<-1+2n_{18})\right)\text{ or }\left(y>\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(|y|<1)\text{ and }n_{4}\text{bmod}2=1\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}<-1+2n_{18})\text{ and }not(y>-1)\right)\right)\text{ or }\left(\left(y>\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(|y|<1)\right)\text{ and }\left(y<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=0\text{ and }not(n_{4}<-1+2n_{18})\text{ and }not(|y|<1)\right)\right)\right)\text{ or }\left(\left(y>\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(|y|<1)\right)\text{ and }\left(n_{4}\text{bmod}2=0\text{ and }not(n_{4}<-1+2n_{18})\text{ and }not(y<1)\right)\right)\right)\text{ or }\left(\left(y>\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(|y|<1)\right)\text{ and }\left(y<\left(-1\right)\left(-1\right)^{\left(-1\right)n_{4}}\text{ and }n_{4}\text{bmod}2=1\text{ and }not(n_{4}<-1+2n_{18})\text{ and }not(y<1)\right)\right)\right)\text{ or }\left(\left(y>\left(SinI(\frac{1}{2}\pi \left(\left(-2\right)n_{4}+1\right))\right)^{-1}\text{ and }\exists n_{24}\in \mathrm{Z}\text{ : }n_{4}=\left(-2\right)n_{24}\text{ and }not(n_{4}>1+2n_{18})\text{ and }not(|y|<1)\right)\text{ and }\left(not(n_{4}<2n_{18}+1)\text{ and }not(|y|<1)\right)\right)\right)\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\pi +2n_{18}\pi +\left(-1\right)arcSin(y^{-1})=\frac{1}{2}\pi +\pi n_{1}
解 y
y=\frac{1}{\sin(x)}
\exists n_{1}\in \mathrm{Z}\text{ : }\left(x>\frac{\pi n_{1}}{2}\text{ and }x<\frac{\pi n_{1}}{2}+\frac{\pi }{2}\right)
共享
已復制到剪貼板
示例
二次方程式
{ x } ^ { 2 } - 4 x - 5 = 0
三角學
4 \sin \theta \cos \theta = 2 \sin \theta
線性方程
y = 3x + 4
算術
699 * 533
矩陣
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
聯立方程
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
微分
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
積分
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
限制
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}