A mechanical linkage tracks an angular displacement θ\thetaθ such that its extension EEE is modelled by the function
E(θ)=−2csc(θ+π) E(\theta) = -2 \csc(\theta + \pi) E(θ)=−2csc(θ+π)for 0≤θ≤2π0 \le \theta \le 2\pi0≤θ≤2π.
Sketch the graph of EEE against θ\thetaθ, stating the equations of any vertical asymptotes and the coordinates of the local turning points.
