Confusing Parametrization

Question

Problem:

Determine whether the following statement is true:

The line $y=3x$ can be parameterized as $$x=\cos (2t)$$ $$y=3\cos(2t)$$ $$-\infty<t<\infty$$

Plugging in for $y$ and $x$ in the equation $y=3x$, I get $3\cos(2t)=3\cos(2t)$, which is true for all $-\infty<t<\infty$. But I am wrong. I need help understanding how to solve this problem.

Answer 1

Due to the fact that $\cos(2t)\in[-1,1]$, the line $y = 3x$ is not parametrized by $x = \cos(2t)$ and $y = 3\cos(2t)$. In fact, what is being parametrized is the line segment

$$L = \{(x,y)\in[-1,1]\times[-3,3]\mid y = 3x\}$$