MAT112 Calculus 2 Professor Porter Sample Test #5 Polar Coordinates

 

  1. Change (5,-3) to polar coordinates.
  2. If r=5 and θ=3π/2
  3. Graph the polar function θ=3π/2
  4. Graph the polar function r = 3 + sin θ
  5. Graph r = 3 cos θ
  6. Graph the parametric equations x = t + 2 y = t(t+4)
  7. Find the Tangent line at the time t = 2 for the above.
  8. Calculate the arclength of the curve r = 3 from 0 to 2π
  9. Find the region enclosed by r = 1 + sin θ
  10. Find the region inside r = 2 2cos θ and r = 4
  11. Sketch the graphs of the following:

  1. Determine the shape of the graph:
  2. Graph the function and describe its shape: r = 2 / (2 + 3 sin θ )