6-6 Converting Polar & Rectangular Equations

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

•  $\theta=\frac{5\pi}{6}$  

•  $\cot\theta=2$  

•  $\cot\theta=5$  

•  $\theta=\frac{3\pi}{4}$  

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.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.B.3

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

Convert the rectangular equation to polar form.
 $x^2+\left(y-2\right)^2=4$ 

•  $r=4\sin\theta$ 

•  $r=6\sin\theta$ 

•  $r=-2\cos\theta+4\sin\theta$ 

•  $r=-4\cos\theta-2\sin\theta$ 

Tags

CCSS.HSG.GPE.A.1

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

•  $y=-\frac{x\sqrt{3}}{3}$ 

•  $y=\frac{x}{4}$ 

•  $y=x$ 

•  $y=-x\sqrt{3}$ 

Tags

CCSS.HSF.TF.A.3

Convert the polar equation to rectangular form.
 $r=2\tan\theta\sec\theta$ 

•  $y=\frac{x^2}{2}$ 

•  $x=y^2$ 

•  $y=\frac{x^2}{4}$ 

•  $x=\frac{y^2}{4}4$ 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Convert the polar equation to rectangular form.
 $\cot\theta=5$ 

•  $y=\frac{x}{5}$ 

•  $y=x\sqrt{3}$ 

•  $y=x$ 

•  $y=5x$ 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Convert the polar equation to rectangular form.
 $r=-4\sin\theta$ 

•  $\left(x-2\right)^2+\left(y-1\right)^2=5$ 

•  $\left(x-1\right)^2+\left(y-3\right)^2=10$ 

•  $\left(x+1\right)^2+\left(y-2\right)^2=5$ 

•  $x^2+\left(y+2\right)^2=4$ 

Tags

CCSS.HSG.GPE.A.1

Convert the polar equation to rectangular form.
 $r=4\cos\theta-2\sin\theta$ 

•  $\left(x+2\right)^2+y^2=4$ 

•  $\left(x-2\right)^2+\left(y-1\right)^2=5$ 

•  $\left(x-2\right)^2+\left(y+1\right)^2=5$ 

•  $\left(x-1\right)^2+y^2=1$ 

Tags

CCSS.HSA.SSE.B.3

CCSS.HSG.GPE.A.1