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) (

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?Responses​The distance is increasing for  0≤𝜃≤𝜋2, because 𝑓⁡(𝜃) is positive and increasing on the interval.​The distance is increasing for  0 less or equal than theta less or equal than pi over 2 , because  f open parentheses theta close parentheses  is positive and increasing on the interval.​The distance is increasing for  3⁢𝜋2≤𝜃≤11⁢𝜋6, because 𝑓⁡(𝜃) is negative and increasing on the interval.​The distance is increasing for  fraction numerator 3 pi over denominator 2 end fraction less or equal than theta less or equal than fraction numerator 11 pi over denominator 6 end fraction , because  f open parentheses theta close parentheses  is negative and increasing on the interval.​The distance is decreasing for  0≤𝜃≤𝜋2, because 𝑓⁡(𝜃) is positive and decreasing on the interval.​The distance is decreasing for  0 less or equal than theta less or equal than pi over 2 , because  f open parentheses theta close parentheses  is positive and decreasing on the interval.​The distance is decreasing for  3⁢𝜋2≤𝜃≤11⁢𝜋6, because 𝑓⁡(𝜃) is negative and decreasing on the interval.

A graph in polar coordinates is of the form: r = -2 cos⁡θ - 4 sin⁡θ. Identify the graph of this function. Hint: Multiply both sides by r and then convert to Cartesian form.  a. Circle b. Ellipse c. Hyperbola  d. Line e. Parabola

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?

Two points are given in polar coordinates by (r,)=(2.00 m, 50.0°) and (r, ) = (5.00 m, 250.0°),respectively.What is the distance between them?

Use the Distance Formula d = r12 + r22 − 2r1r2 cos(𝜃1 − 𝜃2) to find the distance between the two points in polar coordinates. (Round your answer to one decimal place.) 5, 5𝜋6,    7, 𝜋3