Step 1 Answer for sub question a: Given x = 20 cos t, y = 10 sin t To find the cartesian equation that represents the race track the car is going on solve for t using the equation of y. \(y = 10 \sin t\)

\(\frac{y}{10} \sin t\)

\(t = \sin^{−1} (\frac{y}{10})\) Further substitute the value of t in the equation of x. \(x = 20 \cos (\sin^{−1} \frac{y}{10})\) Thus we have found the cartesian equation that represents the race track the car is going on. Step 2 Answer for sub question b: The parametric equations we would use to make the car go three times as faster on the same track is \(x(t)=20 cost(3t), y(t)=10 sin(3t).\) Step 3 Answer for sub question c: The parametric equations we would use to make the car go half as fast on the same track is \(x = 20 \cos (\frac{t}{2}), y = 10 \sin (\frac{t}{2})\)