Exam 9: Parametric Equations Polar Coordinates and Conic Sections

Find an equation of y as a function of x for the parametric equations given below by eliminating the parameter. Also, indicate the direction of the curve. $x = \sin t , \quad y = \cos 2 t , \quad t \in \left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$

Find the polar coordinates of the point (2, -2) given in rectangular coordinates for $\theta \in [ 0,2 \pi ]$ and $r \geq 0$

Find an equation of y as a function of x for the parametric equations given below by eliminating the parameter. Also, indicate the direction of the curve. $x = - 2 t - 1 , \quad y = 3 t ^ { 2 } + 2 , \quad t \in ( - \infty , \infty )$