Show that the equation 4cosα+1=3sinαtanα4\cos \alpha + 1 = 3 \sin \alpha \tan \alpha4cosα+1=3sinαtanα can be written in the form 7cos2α+cosα−3=07\cos^2 \alpha + \cos \alpha - 3 = 07cos2α+cosα−3=0
A light-sensitive robotic arm measures the angle ϕ\phiϕ (in radians) of incoming radiation. The arm reaches a steady state when ϕ\phiϕ satisfies: 4cos3ϕ+1=3sin3ϕtan3ϕ4\cos 3\phi + 1 = 3 \sin 3\phi \tan 3\phi4cos3ϕ+1=3sin3ϕtan3ϕ Determine all possible values for ϕ\phiϕ in the interval 0≤ϕ<2π30 \le \phi < \frac{2\pi}{3}0≤ϕ<32π, giving your answers to 2 decimal places.