Consider the graph of the polar function 𝑟=𝑓⁡(𝜃), where 𝑓⁡(𝜃)=1+2⁢sin⁡𝜃, in the polar coordinate system for 0≤𝜃≤2⁢𝜋. Which of the following statements is true about the distance between the point with polar coordinates (𝑓⁡(𝜃),𝜃) and the origin?

The polar function r = f(q ) , where f(q ) = 1 + 2 cos q , is graphed in the polar coordinate system for0 On which of the following intervals of q is the distance between the point with polarcoordinates ( f (q ),q ) and the origin decreasing?(A) (0, 2.094 ) only(B) (2.094, 4.189 )(C) ((D) (

The figure shows the graph of the polar function 𝑟=𝑓⁡(𝜃), where 𝑓⁡(𝜃)=4⁢cos⁡(2⁢𝜃), in the polar coordinate system for 0≤𝜃≤2⁢𝜋. There are five points labeled 𝐴, 𝐵, 𝐶, 𝐷, and 𝐸. If the domain of 𝑓 is restricted to  0≤𝜃≤𝜋2, the portion of the given graph that remains consists of two pieces. One of those pieces is the portion of the graph in Quadrant I from 𝐶 to 𝐸. Which of the following describes the other remaining piece?

The distance of the point (a cos θ, a sinθ) from the origin is

Refer to distance (𝑥) − 𝑡𝑖𝑚𝑒 (𝑡) graph.Which of the following is incorrect?(a) At D, velocity is positive.(b) At F, motion is in the – 𝑥 direction(c) At C, velocity is +𝑣𝑒(d) All of thes

Determine if the following statement makes sense:After plotting the point with rectangular coordinates ​(0,−​4), a student found polar coordinates without having to show any work.Group of answer choicesThe statement does not make sense because the point ​(0,−​4) is already in the form of the polar coordinates.The statement does not make sense because it is not possible to find the polar coordinates without using the formula for the polar representation.The statement does make sense because the point ​(0,−​4) is represented the same way in polar coordinates.The statement does make sense because the coordinate of the rectangular 𝑥−coordinates is 0.