Show that the equation
4cosα+1=3sinαtanα 4\cos \alpha + 1 = 3 \sin \alpha \tan \alpha 4cosα+1=3sinαtanαcan be written in the form
7cos2α+cosα−3=0 7\cos^2 \alpha + \cos \alpha - 3 = 0 7cos2α+cosα−3=0A 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=3sin3ϕtan3ϕ 4\cos 3\phi + 1 = 3 \sin 3\phi \tan 3\phi 4cos3ϕ+1=3sin3ϕtan3ϕDetermine 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.
