Question

Rewrite the x=sine(t), y=cosine(2t) in Cartesian form.

Answer 1

\[x=\sin{t}\quad,\quad y=\cos{2t}\]\[\cos{2t}=\cos^2{t}-\sin^2{t}=1-2\sin^2{t}\]\[y=1-2x^2\]

Answer 2

For x=sin(t), square both sides. So:
\[x^2 =\sin^2(t) (Eqn. 1)\]

For y=cos(2t), use the identity:
\[\cos(2t) = \cos^2(t)-\sin^2(t) (Eqn. 2)\]

Substitute Eqn. 1 into Eqn. 2:
\[y=\cos^2(t)-x^2\]