In a study of harmonic oscillators, a phase angle ϕ\phiϕ is found to satisfy the equation
4cosecϕ=9cosϕ 4 \operatorname{cosec} \phi = 9 \cos \phi 4cosecϕ=9cosϕfor 0<ϕ<π0 < \phi < \pi0<ϕ<π. Determine the possible values of ϕ\phiϕ, in radians, giving your answers to 3 significant figures.
The configuration of a robotic linkage is governed by the equation
tan3θ−tan20∘1+tan3θtan20∘=2 \frac{\tan 3\theta - \tan 20^\circ}{1 + \tan 3\theta \tan 20^\circ} = 2 1+tan3θtan20∘tan3θ−tan20∘=2for 0∘<θ<180∘0^\circ < \theta < 180^\circ0∘<θ<180∘. Solve this equation to find the possible orientations θ\thetaθ, giving your answers to one decimal place.
