Parametric and Polar Coordinates flashcards

Question 1

What is a parametric curve in the plane?

Accepted Answer

A plane curve given by $x=f(t)$ and $y=g(t)$ for $t$ in an interval; the point $(x(t),y(t))$ traces the curve as $t$ varies.

Question 2

What are polar coordinates $(r,	heta)$?

Accepted Answer

$r$ is the (signed) distance from the origin and $	heta$ is the angle from the positive $x$-axis; a point is represented by $(r,	heta)$.

Question 3

Compute the area inside $r=2\cos	heta$ for $	heta\in\left[-\frac{\pi}{2},\frac{\pi}{2}ight]$.

Accepted Answer

$$A=\frac12\int_{-\pi/2}^{\pi/2} (2\cos	heta)^2\,d	heta=2\int_{-\pi/2}^{\pi/2}\cos^2	heta\,d	heta=\pi$$

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