Polar Point Matching 46C88B
1. The problem asks to match each polar coordinate point $(r, \theta)$ with one of the labeled points A, B, C, or D on the graph.
2. Recall that in polar coordinates, a negative radius $r$ means the point is in the opposite direction of the angle $\theta$. To find the equivalent positive radius and angle, add $\pi$ to $\theta$ and take the absolute value of $r$.
3. The points A, B, C, and D correspond to angles $\pi/6$, $5\pi/6$, $7\pi/6$, and $11\pi/6$ respectively, all with radius 2.
4. Now, match each point:
- (2, $-11\pi/6$): $-11\pi/6$ is coterminal with $\pi/6$ (since $-11\pi/6 + 2\pi = \pi/6$), radius 2, so matches A.
- (-2, $-\pi/6$): Negative radius, so add $\pi$ to angle: $-\pi/6 + \pi = 5\pi/6$, radius 2, matches B.
- (-2, $\pi/6$): Negative radius, add $\pi$: $\pi/6 + \pi = 7\pi/6$, radius 2, matches C.
- (2, $7\pi/6$): Angle $7\pi/6$ with radius 2, matches C.
- (2, $5\pi/6$): Angle $5\pi/6$ with radius 2, matches B.
- (-2, $5\pi/6$): Negative radius, add $\pi$: $5\pi/6 + \pi = 11\pi/6$, radius 2, matches D.
- (-2, $7\pi/6$): Negative radius, add $\pi$: $7\pi/6 + \pi = 13\pi/6$ which is coterminal with $\pi/6$, radius 2, matches A.
- (2, $11\pi/6$): Angle $11\pi/6$ with radius 2, matches D.
Final matches:
9. A
10. B
11. C
12. C
13. B
14. D
15. A
16. D