Exercise 8

  1. Sketch the plane curve with the given vector equation.
  2. Find \(\mathbf{r}'(t)\).
  3. Sketch the position vector \(\mathbf{r}(t)\) and the tangent vector \(\mathbf{r}'(t)\) for the given value of t. \(\mathbf{r}(t) = (\cos t + 1)\mathbf{i} + (\sin t - 1)\mathbf{j}, t=-\pi/3\)