Use the interactive to adjust the values, r and θ, and choose the correct statements based on your observations.The point revolves around the pole when r is changed.The point revolves around the pole counterclockwise when θ is negative.The point revolves around the pole counterclockwise when θ is positive.The point gets closer to or farther from the pole when r is changed.The point gets closer to or farther from the pole when θ is changed.
Answer
A
The point revolves around the pole when r is changed.
B
The point revolves around the pole counterclockwise when θ is negative.
C
The point revolves around the pole counterclockwise when θ is positive.
D
The point gets closer to or farther from the pole when r is changed.
E
The point gets closer to or farther from the pole when θ is changed.
Explanation
In polar coordinates, r sets the point’s distance from the pole, so changing r moves the point closer to or farther from the pole. The angle θ sets the direction: increasing θ in the positive direction rotates the point counterclockwise, while a negative θ rotates it clockwise. Therefore, the correct statements are that a positive θ gives counterclockwise rotation and changing r changes the point’s distance.
AI-written and checked against the verified answer.