Find an Equation of Y as a Function of X $$x = \sin t , \quad y = \cos 2 t , \quad t \in \left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$$

Multiple Choice

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. $$x = \sin t , \quad y = \cos 2 t , \quad t \in \left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$$

A) $y = 1 + 2 x ^ { 2 } , \quad - 1 \leq x \leq 1 , \quad \text { left to right }$
B) $y = 1 - 2 x ^ { 2 } , \quad - 1 \leq x \leq 1 , \quad \text { left to right }$
C) $y = 1 + 2 x ^ { 2 } , \quad - 1 \leq x \leq 1 , \quad \text { right to left }$
D) $y = 1 - 2 x ^ { 2 } , \quad - 1 \leq x \leq 1 , \quad \text { right to left }$