Mathematics

Mathematics

Problem

For which values of θ\theta does the equality arcsin⁡(sin⁡θ)=θ\arcsin(\sin \theta)=\theta hold when θ∈(−π,π)\theta\in(-\pi,\pi)? a) θ∈(−π,0)\theta\in(-\pi,0) b) θ∈(0,π]\theta\in(0,\pi] c) θ∈[−π2,π2]\theta\in\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right] d) θ∈[−π,−π2]∪[π2,π]\theta\in[-\pi,-\tfrac{\pi}{2}]\cup[\tfrac{\pi}{2},\pi]

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