16. Parametric Equations & Polar Coordinates

Plot the point $(3,\(\frac{\pi}{2}\))$ & find another set of coordinates, $(r,θ)$, for this point, where:

(A) $r≥0,2π≤θ≤4π$,

(B) $r≥0,-2π≤θ≤0$,

(C) $r≤0,0≤θ≤2π$.

Plot the point $(-3,-\(\frac{\pi}{6}\))$, then identify which of the following sets of coordinates is the same point.

Plot the point on the polar coordinate system.

$(-2,\(\frac{2\pi}{3}\))$

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.

$r=1-\(\sin\]\theta\)$

Convert each equation to its polar form.

$x^2+(y-2)^2=4$

Plot the point on the polar coordinate system.

$(5,210°)$

Convert the point to polar coordinates.

$(1,1)$

Convert the point to polar coordinates.

$(-2,2)$

Graph $r^2=9\(\sin\)2\(\theta\)$

Convert the point to rectangular coordinates.

$(-3,0)$

Graph $r=1+2\(\sin\]\theta\)$

Convert the point to rectangular coordinates.

$(0,\(\frac{7\pi}{4}\))$

Convert each equation to its polar form.

$y-x=6$

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.

$r^2=-25\(\cos\)2\(\theta\)$

Graph $r=2-2\(\cos\]\theta\)$