An automated tracking sensor for a wind turbine calculates its optimal inclination angle θ\thetaθ relative to the wind direction. For a specific range of wind speeds, the mechanical equilibrium of the sensor is maintained when
Show that the equation
6tanθ=cosθ 6 \tan \theta = \cos \theta 6tanθ=cosθmay be rewritten in the form
sin2θ+6sinθ−1=0 \sin^2 \theta + 6 \sin \theta - 1 = 0 sin2θ+6sinθ−1=0Hence solve, for 0∘≤x≤180∘0^\circ \le x \le 180^\circ0∘≤x≤180∘, the equation
6tan(2x+10∘)=cos(2x+10∘) 6 \tan (2x + 10^\circ) = \cos (2x + 10^\circ) 6tan(2x+10∘)=cos(2x+10∘)giving your answers to 2 decimal places.
