Q:

Sketch parametric curve

An exercise in my textbook asks to sketch the parametrical curve of the following equation:
$$x=e^t\cdot\cos(t)\\y=e^t\cdot\sin(t)\\t\ge0$$
I would usually try to solve one of the equations for t and replace on the other one, or even solve for $\cos(t)$ and $\sin(t)$ and do something like $\cos^2(t)+\sin^2(t)=1$, but both of them wouldn't work...
Can anybody help me?

A:

Note that $x^2 + y^2 = e^{2t}$. So your "radius" is increasing with time, and does not depend on the angle. The curve is a spiral. Choosing a few values of $t$ is good to try to get the picture. See the graph here, down at "parametric plot".

