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ONLY SOLVE THE ONES LEFT BLANK!! GRACIAS AMIGOS Fill all points of intersection

ID: 3348168 • Letter: O

Question

ONLY SOLVE THE ONES LEFT BLANK!! GRACIAS AMIGOS

Fill all points of intersection of the curves r = 2 and r = 2cos(2 Theta). Use the following format to input your answers: Give your answer in polar coordinates (r,theta) with r 0 and 0 Theta 2pi. If the pole is an intersection point, type "pole" in lower case letters in both blanks for the first intersection point. List all other intersection points in order of increasing r. If more than one point has the same value of r, list these points in order of increasing Theta. Type a capital "N" in all unused blanks. First intersection point (r,theta) = ( ) Second intersection point (r,theta) = ( ) Third intersection point (r,theta) = ( ) Fourth intersection point (r,theta) = ( ) Fifth intersection point (r,theta) = ( ) you can earn partial credit on this problem.

Explanation / Answer

There are only two intersection points and they are (2,0) and (2,pi).

For theta = pi/2, r = 2 cos(2theta) = -2, but r>0

Similarly for theta = 3pi/2, r = 2 cos(2theta) = -2 but r>0

Therefore, the only two intersection points are (2,0) and (2,pi). Remaining blacnks should be (N,N) three times.