Test Objectives
• Demonstrate the ability to convert circles from rectangular form to polar form
• Demonstrate the ability to convert circles from polar form to rectangular form
• Demonstrate the ability to graph circles on the polar grid
Circles in Polar Form Practice Test:

#1:

Instructions: Convert each to polar form, then graph the polar equation.

$$a)\hspace{.1em}(x - 1)^2 + (y - 3)^2=10$$

$$b)\hspace{.1em}x^2 + (y - 3)^2=9$$

#2:

Instructions: Convert each to polar form.

$$a)\hspace{.1em}(x + 2)^2 + (y + 2)^2=8$$

$$b)\hspace{.1em}(x - 2)^2 + (y + 1)^2=5$$

#3:

Instructions: Convert each to rectangular form.

$$a)\hspace{.1em}r=4 \hspace{.1em}\text{cos}\left(θ + \frac{π}{3}\right)$$

$$b)\hspace{.1em}r=4 \hspace{.1em}\text{sin}\left(θ + \frac{π}{4}\right)$$

#4:

Instructions: Convert each to rectangular form.

$$a)\hspace{.1em}r=4 \hspace{.1em}\text{cos}\left(θ + \frac{π}{6}\right)$$

$$b)\hspace{.1em}r=2 \hspace{.1em}\text{sin}\left(θ + \frac{π}{6}\right)$$

#5:

Instructions: Convert each to rectangular form.

$$a)\hspace{.1em}r=2 \hspace{.1em}\text{cos}\left(θ + \frac{π}{4}\right)$$

$$b)\hspace{.1em}r=6 \hspace{.1em}\text{sin}\left(θ + \frac{π}{3}\right)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}r=2 \hspace{.1em}\text{cos}\hspace{.1em}θ + 6 \hspace{.1em}\text{sin}\hspace{.1em}θ$$

$$b)\hspace{.1em}r=6 \hspace{.1em}\text{sin}\hspace{.1em}θ$$

#2:

Solutions:

$$a)\hspace{.1em}r=-4 \hspace{.1em}\text{cos}\hspace{.1em}θ - 4 \hspace{.1em}\text{sin}\hspace{.1em}θ$$

$$b)\hspace{.1em}r=4 \hspace{.1em}\text{cos}\hspace{.1em}θ - 2 \hspace{.1em}\text{sin}\hspace{.1em}θ$$

#3:

Solutions:

$$a)\hspace{.1em}(x - 1)^{2}+ (y + \sqrt{3})^{2}=4$$

$$b)\hspace{.1em}(x - \sqrt{2})^{2}+ (y - \sqrt{2})^{2}=4$$

#4:

Solutions:

$$a)\hspace{.1em}(x - \sqrt{3})^{2}+ (y + 1)^{2}=4$$

$$b)\hspace{.1em}\left(x - \frac{1}{2}\right)^{2}+ \left(y - \frac{\sqrt{3}}{2}\right)^{2}=1$$

#5:

Solutions:

$$a)\hspace{.1em}\left(x - \frac{\sqrt{2}}{2}\right)^{2}+ \left(y + \frac{\sqrt{2}}{2}\right)^{2}=1$$

$$b)\hspace{.1em}\left(x - \frac{3\sqrt{3}}{2}\right)^{2}+ \left(y - \frac{3}{2}\right)^{2}=9$$