Graph Polar & Rectangular Equations

Which equation represents the polar graph?

• r = 6 + 6 sin θ
• r = 12 sin θ
• r = 4 - 3 sin θ
• r = 4 + 5 sin θ

Which equation represents the polar graph?

• r = sin θ
• r = sin 4θ
• r = 4 sin θ
• r = 4 cos θ

To change from (x,y) form to  $\left(r,\ \theta\right)$  form or rectangular to polar you need to know which two facts?

•  $r\ comes\ from\ x^2+y^2=r^2$  

•  $r\ comes\ from\ r\ =\ \tan\theta$  

•  $\theta\ comes\ from\ \cos^2\theta\ +\sin^2\theta\ =\ 1$  

•  $\theta\ comes\ from\ \tan\theta=\frac{y}{x}$  

Convert the rectangular equation to polar form.
 $y=\frac{x}{2}$  

•  $\theta=\frac{5\pi}{6}$  

•  $\cot\theta=2$  

•  $\cot\theta=5$  

•  $\theta=\frac{3\pi}{4}$  

Tags

CCSS.HSF-BF.B.4A

Convert the rectangular equation to polar form.
 $y=-x\sqrt{3}$  

•  $\cot\theta=2$  

•  $\tan\theta=1$  

•  $\cot\theta=5$  

•  $\theta=\frac{2\pi}{3}$  

Tags

CCSS.HSF-BF.B.4A

Convert the rectangular equation to polar form.
 $\left(x-3\right)^2+y^2=9$  

•  $r=6\cos\theta$  

•  $r=-2\cos\theta+6\sin\theta$  

•  $r=6\cos\theta+2\sin\theta$  

•  $r=-6\sin\theta$  

Tags

CCSS.HSG.GPE.A.1

Convert the rectangular equation to polar form.
 $x^2+y^2=16$  

•  $r=4$  

•  $r=16$  

•  $r=4\cos\theta+4\sin\theta$  

•  $r=4\sin\theta$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSG.GPE.A.1

Which are the two equations we use for converting from polar to rectangular?

• $x=r\cos\theta$

• $x=v\sin\theta$

• $y=r\sin\theta$

• $y=vt\cos\theta$

Convert the polar equation to rectangular form.
 $\theta=\frac{5\pi}{6}$ 

•  $y=-\frac{x\sqrt{3}}{3}$ 

•  $y=\frac{x}{4}$ 

•  $y=x$ 

•  $y=-x\sqrt{3}$ 

If the polar equation is  $r\ =5$  , what is the rectangular equaiton?

•  $x\ +y=5$  

•  $r=5\cos\theta$  

•  $x^2+y^2=25$  

•  $\tan\theta=5$