A wave profile in a simulated fluid environment is represented by the function H(ϕ)=tan(3π2−ϕ)\displaystyle H(\phi) = \tan\left(\frac{3\pi}{2} - \phi\right)H(ϕ)=tan(23π−ϕ) for 0≤ϕ≤2π0 \le \phi \le 2\pi0≤ϕ≤2π.
Sketch the graph of y=H(ϕ)y = H(\phi)y=H(ϕ), clearly indicating the equations of the vertical asymptotes and the coordinates of any points where the graph crosses the horizontal axis.