h/sin(180-alpha)=h/sin(alpha) Denklemini Çözme

$$\frac { h } { \sin ( 180 - \alpha ) } = \frac { h } { \sin ( \alpha ) }$$

h için çözün (complex solution)

$$\left\{\begin{matrix}h=0\text{, }&\nexists n_{2}\in \mathrm{Z}\text{ : }\alpha =\pi n_{2}\text{ and }\nexists n_{3}\in \mathrm{Z}\text{ : }\alpha =180-\pi n_{3}\\h\in \mathrm{C}\text{, }&\frac{i}{e^{180i-i\alpha }}-ie^{180i-i\alpha }-2\sin(\alpha )=0\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }\alpha =\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =180-\pi n_{1}\end{matrix}\right,$$

h için çözün

$$\left\{\begin{matrix}h=0\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}+180-57\pi \text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }\alpha =\pi n_{2}\\h\in \mathrm{R}\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\alpha =\pi n_{3}+\arcsin(\frac{\sin(180)}{\sqrt{2\left(\cos(180)+1\right)}})+\pi \end{matrix}\right,$$

α için çözün

$$\left\{\begin{matrix}\\\alpha =\pi n_{2}+\arcsin(\frac{\sin(180)\sqrt{\frac{2}{\cos(180)+1}}}{2})+\pi \text{, }n_{2}\in \mathrm{Z}\text{, }&\text{unconditionally}\\\alpha \notin \pi n_{1}+180-57\pi ,\pi n_{1}\text{, }\forall n_{1}\in \mathrm{Z}\text{, }&h=0\end{matrix}\right,$$