Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Problem
Problem Let θ , ϕ ∈ [ 0 , 2 π ] \theta, \phi \in [0, 2\pi] θ , ϕ ∈ [ 0 , 2 π ] 2 cos θ ( 1 − sin ϕ ) = sin 2 θ ( tan θ 2 + cot θ 2 ) cos ϕ − 1 , 2 \cos \theta (1 - \sin \phi) = \sin^2 \theta \left( \tan \frac{\theta}{2} + \cot \frac{\theta}{2} \right) \cos \phi - 1, 2 cos θ ( 1 − sin ϕ ) = sin 2 θ ( tan 2 θ + cot 2 θ ) cos ϕ − 1 , tan ( 2 π − θ ) > 0 \tan(2\pi - \theta) > 0 tan ( 2 π − θ ) > 0 − 1 < sin θ < − 3 2 -1 < \sin \theta < -\frac{\sqrt{3}}{2} − 1 < sin θ < − 2 3 ϕ \phi ϕ 0 < ϕ < π 2 0 < \phi < \frac{\pi}{2} 0 < ϕ < 2 π π 2 < ϕ < 4 π 3 \frac{\pi}{2} < \phi < \frac{4\pi}{3} 2 π < ϕ < 3 4 π 4 π 3 < ϕ < 3 π 2 \frac{4\pi}{3} < \phi < \frac{3\pi}{2} 3 4 π < ϕ < 2 3 π 3 π 2 < ϕ < 2 π \frac{3\pi}{2} < \phi < 2\pi 2 3 π < ϕ < 2 π Browse the problem library