Solve sinθgeqcosphi

$$\sin \theta \geq \cos \phi$$

Solve for ϕ

$$\left\{\begin{matrix}\\ϕ\in \begin{bmatrix}\frac{-2\arcsin(\sin(\theta ))+4\pi n_{2}+\pi }{2},\frac{2\arcsin(\sin(\theta ))+4\pi n_{2}+3\pi }{2}\end{bmatrix}\text{, }n_{2}\in \mathrm{Z}\text{, }&\text{unconditionally}\\ϕ\in \mathrm{R}\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\theta =2\pi n_{3}+\frac{\pi }{2}\text{, }not(n_{1}>n_{3})\text{ or }\theta >2\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Solve for θ

$$\theta \in \begin{bmatrix}\arcsin(\cos(ϕ))+2\pi n_{1},-\arcsin(\cos(ϕ))+2\pi n_{1}+\pi \end{bmatrix}\text{, }n_{1}\in \mathrm{Z}$$