(Solved): 17.5 Eliminate the parameter \( t \) to write an equation containing only \( x \) and \( y \). The ...

17.5

Eliminate the parameter \( t \) to write an equation containing only \( x \) and \( y \). Then report the domain and range of the graph. \[ \begin{array}{l} x=\sin 5 t \\ y=6 \cos 10 t \end{array} \] Hint: the identity \( \cos 2 \theta=1-2 \sin ^{2} \theta \) is useful here. (a) Write the equation in terms of only \( x \) and \( y \) \[ y=6(1+x)^{2} \] \[ y=6-12 x^{2} \] \[ y=6(1-x)^{2} \] \[ y=6+6 x^{2} \] \[ y=12 x^{2}-6 \] \[ x^{2}+\frac{y^{2}}{36}=1 \] \[ y=6-6 x \] \[ y=12 x \] \[ y=6+6 x \] \[ y=\frac{1}{6} x^{2} \] (b) Report the domain of the graph. The domain is \( 0