Polar

Convert the polar coordinates to rectangular form  $\left(6,\ \frac{2\pi}{3}\right)$  

• ( -3, 3)

• (3, 3√3)

• (-3, 3√3)

• (3, -3√3)

Tags

CCSS.HSN.CN.B.4

What is the equation?

• Θ = π/4

• Θ = -5π/4

• Θ = -3π/4

• Θ = 5π/4

Tags

CCSS.HSN.CN.B.4

Which point represents (-4, π/2)

• D
• C
• B
• A

Tags

CCSS.HSN.CN.B.4

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.HSN.CN.B.4

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.HSN.CN.B.4

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.HSN.CN.B.4

If z = 2(cos(20) + isin(20)) and w = 3(cos(105) + isin(105)), find z ⋅ w

• 3/2(cos(85) + isin(85))
• 3/2(cos(125) + isin(125))
• 6(cos(85) + isin(85))
• 6(cos(125) + isin(125))

Tags

CCSS.HSN.CN.B.4

Given the polar point (6, π/9), find an equivalent polar point using a negative angle.

• (6, -π/9)
• (6, -17π/9)
• (6, -10π/9)
• (-6, -π/9)

Tags

CCSS.HSN.CN.B.4

Find the formula for the 4th roots of  $5\left[\cos\ 60\degree\ +\ i\ \sin\ 60\degree\right]$  

•  $4^{\frac{1}{5}}\left[\cos\ \left(5\degree+\ 90k\degree\right)\ +\ i\ \sin\left(5\degree+\ 90k\degree\right)\ \right]$  

•  $5^{\frac{1}{4}}\left[\cos\ \left(15\degree+\ 90k\degree\right)\ +\ i\ \sin\left(15\degree+\ 90k\degree\right)\ \right]$  

•  $5^{\frac{1}{4}}\left[\cos\ \left(30\degree+\ 180k\degree\right)\ +\ i\ \sin\left(30\degree+\ 180k\degree\right)\ \right]$  

•  $\ \ \ 5^4\left[\cos\ \left(60\degree+\ 90k\degree\right)\ +\ i\ \sin\left(15\degree+\ 90k\degree\right)\ \right]$  

Tags

CCSS.HSN.CN.B.4

Find z/w when  $z\ =\ \frac{1}{2}\left(\cos\ 60\degree\ +\ i\ \sin\ 60\degree\right)$  and  $w\ =\ 3\ \left(\cos\ 30\degree\ +\ i\ \sin\ 30\degree\right)$  

• $\frac{\sqrt{3}}{12}+\ \frac{1}{12}\ i$

• $12\sqrt{3}+\ 3i$

• $\frac{\sqrt{3}}{12}-\ \frac{1}{12}\ i$

• $12\sqrt{3}-12i$

Tags

CCSS.HSN.CN.B.4