Quick Check Polar to Rectangular

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.

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

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

•  $\left(\sqrt{3},\ 1\right)$  

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

•  $\left(1,\ \sqrt{3}\right)$  

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

•  $r\ comes\ from\ x^2+y^2=r^2$  

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

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

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

Do the rectangular points (3, -2) and (3, 2) have the same polar coordinates?  Choose the best answer.

• yes, because you square the x and y values.

• no, the r values will be the same but angle theta will be different because the points are in different quadrants. 

• no, both r and angle theta are different.

Given the rectangular point  $\left(-3,\ 0\right)$  , find the value of r.

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

•  $x\ +y=5$  

•  $r=5\cos\theta$  

•  $x^2+y^2=25$  

•  $\tan\theta=5$  

Find the polar coordinates of the rectangular point. (0,3)

• (3,π)
• (3,0)
• (3,π/2)
• (3,-3π/2)

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSG.C.B.5

Convert the rectangular coordinates to polar coordinates
(6√3, 6)

• (12, π/6)
• (6, 7π/6)
• (6, π/6)
• (12, 7π/6)

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSG.C.B.5

CCSS.HSN.CN.B.4

Which point represents (2, π/6)

• F
• E
• B
• A