Revison and HW Polar coordinates

 $\theta\ =\ -\pi$  

 $\theta\ =\ -2\pi+\frac{\pi}{8}$  

 $-2\pi-\frac{\pi}{8}$  

0

 $\theta\ =\ -\pi$  

 $\theta\ =\ -2\pi+\frac{\pi}{8}$  

 $-2\pi-\frac{\pi}{8}$  

0

 $-240^o$  

 $-60^o$  

 $840^o$  

 $240^o$  

 $(2,-\frac{π}{6})$  

 $(-2,\frac{5π}{6})$  

 $(2,\frac{11π}{6})$  

 $(-2,\frac{11π}{6})$  

F

E

B

A

Always True

Sometimes True.

Never True.

How can I tell when the coordinates are not given?

 $\left(0,2\pi\right)\ \$  

 $\left(0,2021\pi\right)\$  

 $\left(1,0\right)\$  

 $\left(0,0\right)$  

$r=4$

$r=8$

$\theta=2\pi$

 $r\ =\ -4$ 

Θ =- π/4

Θ = -5π/4

Θ = 3π/4

Θ = 5π/4

2

4

$0.9$

2.01

Symmetry with respect to the polar axis.

Symmetry with respect to  $\theta=\frac{\pi}{2}$  

Symmetry with respect to the Pole.

No evident symmetry.

Symmetry with respect to the polar axis.

Symmetry with respect to  $\theta=\frac{\pi}{2}$  

Symmetry with respect to the Pole.

No evident symmetry.

None

1

2

3

4

$r=2\cos4\theta$

$r=2\sin4\theta$

$r=4\cos2\theta$

$r=2\cos8\theta$

 $r=3\cos\theta$  

 $r=\cos3\theta$  

 $r=2$  

 $r=3\theta$  

$r=-\frac{3}{2}\cos\theta$

$r=\frac{3}{2}\cos\theta$

$r=-\frac{3}{2}\sin\theta$

$r=\frac{3}{2}\sin\theta$

$r=-\sin\theta$

$r=0.5\sin\theta$

$r=-\cos\theta$

$r=-0.5\sin\theta$

$r^2=4\cos2\theta$

$r=4\cos^2\theta$

$r^2=\sin4\theta$

$r^2=4\sin2\theta$

$r^2=16\sin2\theta$

$r^2=16\cos2\theta$

$r^2=4\sin2\theta$

$r^2=4\cos2\theta$

1

2

3

4