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Parametric Equations and Polar Coordinates
  
 
Problems
Problem 1.1: Is the following plane curve a function: y = 3t2, x =
, 0≤t≤5? [Solution]
Problem 1.2: The following plane curve is a circle: x = 2 cos(t), y = 2 sin(t), 0≤t < 2π. Is its orientation clockwise or couterclockwise? What happens when you reverse the parametric equations, so that x = 2 sin(t), y = 2 cos(t)? [Solution]
Problem 1.3: Convert the parametric equation x = 2t, y =
, t > 0, to a rectangular equation. [Solution]
Problem 1.4: Convert the parametric equation x = 3t + 1, y =
, t
, to a rectangular equation. [Solution]
Problem 1.5: How many times does the graph of x = t2 - t - 6, y = 2t, -5 < t < 5 cross the y-axis? [Solution]
Problem 1.6: Jim and Bob are racing from the origin to the point (5, 10). Let t be the number of seconds after the start of the race. Jim's position at any time t is given by the parametric equations x = t, y = 2t. Bob's position at any time t is given by the parametric equations x = 5t, y = 10t. Who will win the race? How long does it take each competitor to finish the race? [Solution]
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