Give parametric equations and bounds for the parameter that describe the unit circle as shown. In each case the unit circle should be traced only once. Check the answers by putting them in a calculator and seeing if we find the right picture.
We want to trace the unit circle starting from the usual point and going in the same direction as usual. However, we want to trace it very slowly, taking 8π to go around instead of 2π. Take the usual parameterization and make the period of each equation 4 times longer:
Since we want to take 8π to go around the full circle, we need0≤ t ≤ 8π.