Test Objectives
  • Demonstrate the ability to convert a line from rectangular form to polar form
  • Demonstrate the ability to convert a line from polar form to rectangular form
  • Demonstrate the ability to graph a line on the polar coordinate plane
Polar Form of a Line Practice Test:

#1:

Instructions: Convert to polar form, then graph on the polar grid.

$$a)\hspace{.1em}y=x$$

$$b)\hspace{.1em}y=\frac{x\sqrt{3}}{3}$$


#2:

Instructions: Graph on the polar grid, then convert to rectangular form.

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

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


#3:

Instructions: Convert to rectangular form.

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

$$b)\hspace{.1em}r=4 \hspace{.1em}\text{sec}\left(θ + 45°\right)$$


#4:

Instructions: Convert to rectangular form.

$$a)\hspace{.1em}r=3 \hspace{.1em}\text{sec}(θ + 60°)$$

$$b)\hspace{.1em}r=3 \hspace{.1em}\text{sec}\hspace{.1em}θ$$


#5:

Instructions: Convert to rectangular form.

$$a)\hspace{.1em}r=4 \hspace{.1em}\text{csc}\hspace{.1em}θ$$

$$b)\hspace{.1em}r=\text{sec}(θ + 45°)$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}θ=45°$$

Graphing θ=45°

$$b)\hspace{.1em}θ=30°$$

Graphing θ=45°

#2:

Solutions:

$$a)\hspace{.1em}y=-x - 2\sqrt{2}$$

Graphing r=-2csc(θ + π/4)

$$b)\hspace{.1em}y=-\frac{x\sqrt{3}}{3}+ \frac{4\sqrt{3}}{3}$$

Graphing r=2csc(θ + π/6)

#3:

Solutions:

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

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


#4:

Solutions:

$$a)\hspace{.1em}y=\frac{x\sqrt{3}}{3}- 2\sqrt{3}$$

$$b)\hspace{.1em}x=3$$


#5:

Solutions:

$$a)\hspace{.1em}y=4$$

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