The path of a particle is given by r(t) = tsin(t) * i - tcos(t) * j where t≥0. The particle leaves the origin at t = 0 and then spirals outwards. Let θ be the acute angle at which the path of the particle crosses the x-axis. Find tan(θ) when t = 3pi/2. I was able to figure out a few things: At t = 3pi/2, the particle crosses the x-axis for a second time (first being at t = pi/2). At t = 3pi/2, the speed of the particle is (1/2)sqrt(9*pi^2 + 4). Tan(θ) = gradient = dy/dx Other than that, I don't know where to start or what to do.