حل y=sinθ+sqrt{1-sin^2θ}

$$y = \sin \theta + \sqrt { 1 - \sin ^ { 2 } \theta }$$

حل مسائل y

$$y=|\cos(\theta )|+\sin(\theta )$$

حل مسائل θ

$$\left\{\begin{matrix}\theta =-\arcsin(\frac{\sqrt{2-y^{2}}+y}{2})+2\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}\text{; }\theta =\arcsin(\frac{\sqrt{2-y^{2}}+y}{2})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&y\geq 1\text{ and }y\leq \sqrt{2}\\\theta =-\arcsin(\frac{-\sqrt{2-y^{2}}+y}{2})+2\pi n_{3}+\pi \text{, }n_{3}\in \mathrm{Z}\text{; }\theta =\arcsin(\frac{-\sqrt{2-y^{2}}+y}{2})+2\pi n_{4}\text{, }n_{4}\in \mathrm{Z}\text{, }&y\geq -1\text{ and }|y|\leq \sqrt{2}\end{matrix}\right.$$