NYJC Graphing Techniques Tutorial Q8

Sketch the curves given parametrically by the following equations and find the Cartesian equations of these curves:

1. \(x=1-t\), \(y=2{{t}^{2}}\), where \(t<1\)
2. \(x=\sin \theta +1\), \(y=\frac{1}{2}\cos \theta \), where \(-\frac{\pi }{2}\le \theta <0\)
3. \(x=\tan t\), \(y=\sin t\), \(0 < t < \frac{\pi }{2}\)
4. \(x=\frac{1}{2}\left( {{\mathrm{e}}^{3t}}+2{{\mathrm{e}}^{-3t}} \right)\), \(y=\frac{1}{2}\left( {{\mathrm{e}}^{3t}}-2{{\mathrm{e}}^{-3t}} \right)\)