Converting Between Polar and Rectangular

Convert the polar coordinate to a rectangular coordinate:

 $\left(6,\frac{\pi}{2}\right)$  

• (6,0)

• (0,6)

• (-6,0)

• (0,-6)

Convert the polar coordinate to a rectangular coordinate:

 $\left(1,\frac{7\pi}{4}\right)$  

•  $\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$  
  

•  $\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$  
  

•  $\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$  

•  $\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$  

Convert the polar coordinate to a rectangular coordinate:

 $\left(-1,-\frac{7\pi}{4}\right)$  

•  $\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$  
  

•  $\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$  
  

•  $\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$  

•  $\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$  

Convert the polar coordinate to a rectangular coordinate:

 $\left(4,-\frac{\pi}{3}\right)$  

•  $\left(2,2\sqrt{3}\right)$  
  

•  $\left(2,-2\sqrt{3}\right)$  
  

•  $\left(2\sqrt{3},2\right)$  
  

•  $\left(2\sqrt{3},-2\right)$  
  

Convert the rectangular coordinate into a polar coordinate.

 $\left(-3,3\right)$  

•  $\left(\sqrt{18},\frac{3\pi}{4}\right)$  

•  $\left(\sqrt{18},\frac{7\pi}{4}\right)$  

•  $\left(4,\frac{7\pi}{6}\right)$  

•  $\left(4,\frac{11\pi}{6}\right)$  

Convert the rectangular coordinate into a polar coordinate.

 $\left(-3\sqrt{3},-3\right)$  

•  $\left(\sqrt{18},\frac{3\pi}{4}\right)$  

•  $\left(\sqrt{18},\frac{7\pi}{4}\right)$  

•  $\left(6,\frac{7\pi}{6}\right)$  

•  $\left(6,\frac{11\pi}{6}\right)$  

Convert the rectangular coordinate into a polar coordinate.

 $\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$  

•  $\left(1,\frac{5\pi}{3}\right)$  

•  $\left(1,\frac{\pi}{3}\right)$  

•  $\left(4,\frac{3\pi}{2}\right)$  

•  $\left(4,\frac{\pi}{2}\right)$  
  

Convert the rectangular coordinate into a polar coordinate.

 $\left(0,-4\right)$  

•  $\left(1,\frac{5\pi}{3}\right)$  

•  $\left(1,\frac{\pi}{3}\right)$  

•  $\left(4,\frac{3\pi}{2}\right)$  

•  $\left(4,\frac{\pi}{2}\right)$  
  

Given the polar equation $r=3\sin\left(\theta\right)$ , select the correct x-equation.

•  $x=3\sin^2\left(\theta\right)$  

•  $x=3\sin\left(\theta\right)\cos\left(\theta\right)$  

•  $x=3\sin\left(\theta\right)\tan\left(\theta\right)$  

•  $x=3\sin\left(\theta\right)\sec\left(\theta\right)$  

Given the polar equation $r=3\sin\left(\theta\right)$ , select the correct y-equation.

•  $x=3\sin^2\left(\theta\right)$  

•  $x=3\sin\left(\theta\right)\cos\left(\theta\right)$  

•  $x=3\sin\left(\theta\right)\tan\left(\theta\right)$  

•  $x=3\sin\left(\theta\right)\sec\left(\theta\right)$