The angular displacement, ϕ\phiϕ, of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:
11secϕ=32sinϕ 11 \sec \phi = 32 \sin \phi 11secϕ=32sinϕShow that this equation can be expressed in the form sin2ϕ=k\sin 2\phi = ksin2ϕ=k, where k k\,k is a constant to be determined.
Hence, find the smallest positive value of ϕ\phiϕ, in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.
