Converting Between Polar and Rectangular Worksheet with Answer Key

What's on the worksheet

1. Give exact rectangular coordinates for each polar point.
   \left(8, \dfrac{7\pi}{6}\right)\left(-10, \dfrac{2\pi}{3}\right)\left(6, -\dfrac{3\pi}{4}\right)\left(-3, \dfrac{3\pi}{2}\right)\left(2\sqrt{2}, \dfrac{7\pi}{4}\right)
2. Give a polar name with r > 0 and 0 ≤ θ < 2π, exact, for each point.
   (-5\sqrt{3}, 5)(2\sqrt{6}, 2\sqrt{2})(-\sqrt{2}, -\sqrt{6})(1, -\sqrt{3})(0, 9)
3. Give a polar name with r < 0 and 0 ≤ θ < 2π, exact, for each point.
   (-3, 3\sqrt{3})(4, 4)(7\sqrt{3}, -7)
4. A warehouse robot is parked at the origin of the floor grid, which is marked in meters east (x) and north (y).
5. A rotating sprinkler stands at the origin of a park lawn's grid, marked in meters east and north of the sprinkler.
6. The points P = (-2, π6) and Q = (4, π2) are given in polar coordinates, with O the pole.
7. A point has polar name (r, θ) with r > 0 and rectangular coordinates (x, y).