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?

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?

Find the length of the curve over the given interval.polar equationr = 10a cos(𝜃)interval

Convert the rectangular coordinates left parenthesis, 0, comma, 1, right parenthesis(0,1) into polar form. Express the angle using radians in terms of piπ over the interval 0, is less than or equal to, theta, is less than, 2, pi0≤θ<2π, with a positive value of rr.