Math Analysis April 20 - 24 part 2

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.
 $\left(x-3\right)^2+y^2=9$  

•  $r=6\cos\theta$  

•  $r=-2\cos\theta+6\sin\theta$  

•  $r=6\cos\theta+2\sin\theta$  

•  $r=-6\sin\theta$  

Tags

CCSS.HSG.GPE.A.1

Convert the 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.HSN.CN.B.4

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

• $x=r\cos\theta$

• $x=v\sin\theta$

• $y=r\sin\theta$

• $y=vt\cos\theta$

How do we find values for  $\cos\theta\ \ and\ \ \ \sin\theta$  ?

• We look at our trusty unit circle!

• We take a wild guess.

Tags

CCSS.HSF.TF.A.2

Using the formulas on the notes, change the point  $\left(2,\ \frac{\pi}{6}\right)$  into rectangular (x, y) form.

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

•  $\left(\sqrt{3},\ 1\right)$  

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

•  $\left(1,\ \sqrt{3}\right)$  

Tags

CCSS.HSN.CN.B.4

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

•  $x\ +y=5$  

•  $r=5\cos\theta$  

•  $x^2+y^2=25$  

•  $\tan\theta=5$