The foundation of the polar coordinate system consists of a point, called the ____________, and a ray extending out from it, called the ____________.Group of answer choicespolar axis; poleorigin; 𝑥−axispole; polar axis𝑥−axis; origin PreviousNext

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?

Which of the following is the most common coordinate system used in robotics?Polar coordinate systemCartesian coordinate systemCylindrical coordinate systemSpherical coordinate system

Which of the following common polar curves is represented by: ?

Which of the following structures is / are polar?Data:

An angle of measure theta is in standard position with initial ray on the x-axis, vertex at the origin, and terminal ray in Quadrant 2.The terminal ray in Quadrant 2 intersects the circle at point P.A line segment begins at the origin and ends at point R, which lies on the circle in Quadrant 3.A dashed vertical line segment extends from point P to point R. The segment is perpendicular to the x axis.A dashed horizontal line segment extends from point P to a point on the y axis. The segment is perpendicular to the y axis.​​​The figure shows a circle centered at the origin with an angle of measure 𝜃 radians in standard position. The terminal ray of the angle intersects the circle at point 𝑃, and point 𝑅 also lies on the circle. The coordinates of 𝑃 are (𝑥,𝑦), and the coordinates of 𝑅 are (𝑥,-𝑦). Which of the following is true about the sine of 𝜃 ?Responses​ sin⁡𝜃=𝑥5 , because it is the ratio of the horizontal displacement of 𝑃 from the 𝑦-axis to the distance between the origin and 𝑃.​ sin theta equals x over 5  , because it is the ratio of the horizontal displacement of  P  from the  y -axis to the distance between the origin and  P .​ sin⁡𝜃=𝑥5 , because it is the ratio of the horizontal displacement of 𝑅 from the 𝑦-axis to the distance between the origin and 𝑅.​ sin theta equals x over 5  , because it is the ratio of the horizontal displacement of  R  from the  y -axis to the distance between the origin and  R .​​​ sin⁡𝜃=-𝑦5 , because it is the ratio of the vertical displacement of 𝑅 from the 𝑥-axis to the distance between the origin and 𝑅.​​​ sin theta equals fraction numerator negative y over denominator 5 end fraction  , because it is the ratio of the vertical displacement of  R  from the  x -axis to the distance between the origin and  R .​​ sin⁡𝜃=𝑦5 , because it is the ratio of the vertical displacement of 𝑃 from the 𝑥-axis to the distance between the origin and 𝑃.