### Chain Rule & Integration by Substitution

Fluency exercise

Parametric equations for nine curves are defined by combining the row and column headings in the table below. The domain of $t$ for each curve is the set of values of $t$ for which the $x$ and $y$ coordinates are defined.
 $x=\cos t$ $t\in \mathbb{R}$ $x=2t$ $t\in \mathbb{R}$ $x=\tan t$ $-4\pi\leq t\leq 4\pi$ $t\neq \pm\tfrac{\pi}{2}, \pm \tfrac{3\pi}{2}, \pm \tfrac{5\pi}{2}, \pm \tfrac{7\pi}{2}$ $y=2\sin t$ $t\in \mathbb{R}$ $y=t^2$ $t\in \mathbb{R}$ $y=\dfrac{2}{t}$ $-4\pi\leq t \leq 4\pi$ and $t\neq 0$