Test Objectives
  • Demonstrate the ability to plot polar coordinates on the polar grid
  • Demonstrate the ability to convert between polar and rectangular coordinates
  • Demonstrate the ability to find multiple forms for given polar coordinates
Polar Coordinate System Practice Test:

#1:

Instructions: Plot the given polar coordinates and convert to rectangular coordinates.

$$a)\hspace{.1em}(5, 240°)$$

$$b)\hspace{.1em}(4, 45°)$$


#2:

Instructions: Plot the given polar coordinates and convert to rectangular coordinates.

$$a)\hspace{.1em}(3, -240°)$$

$$b)\hspace{.1em}(2, 270°)$$


#3:

Instructions: Convert each pair of rectangular coordinates to polar coordinates and plot.

$$r > 0$$ $$0 ≤ θ < 360°$$

$$a)\hspace{.1em}\left(-\frac{3\sqrt{3}}{2}, \frac{3}{2}\right)$$

$$b)\hspace{.1em}\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$$


#4:

Instructions: Convert each pair of rectangular coordinates to polar coordinates and plot.

$$r > 0$$ $$0 ≤ θ < 360°$$

$$a)\hspace{.1em}(\sqrt{2}, \sqrt{2})$$

$$b)\hspace{.1em}\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$


#5:

Instructions: Find all pairs of polar coordinates that describe the given point.

$$a)\hspace{.1em}(3, 255°)$$

$$b)\hspace{.1em}(-4, 150°)$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\left(-\frac{5}{2}, -\frac{5\sqrt{3}}{2}\right)$$ Plotting (5, 240°) on the polar grid

$$b)\hspace{.1em}(2\sqrt{2}, 2\sqrt{2})$$ Plotting (4, 45°) on the polar grid


#2:

Solutions:

$$a)\hspace{.1em}\left(-\frac{3}{2}, \frac{3\sqrt{3}}{2}\right)$$ Plotting (3, -240°) on the polar grid

$$b)\hspace{.1em}(0, -2)$$ Plotting (2, 270°) on the polar grid


#3:

Solutions:

$$a)\hspace{.1em}(3, 150°)$$ Plotting (3, 150°) on the polar grid

$$b)\hspace{.1em}(1, 210°)$$ Plotting (1, 210°) on the polar grid


#4:

Solutions:

$$a)\hspace{.1em}(2, 45°)$$ Plotting (2, 45°) on the polar grid

$$b)\hspace{.1em}(1, 120°)$$ Plotting (1, 120°) on the polar grid


#5:

Solutions:

$$a)\hspace{.1em}(3, 255° + 360n°)$$ $$\text{and}$$ $$(-3, 75° + 360n°)$$

$$b)\hspace{.1em}(-4, 150° + 360n°)$$ $$\text{and}$$ $$(4, 330° + 360n°)$$