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Test for symmetry with respect to Q=pi/2 , the polar axis and the pole.

r = 16 cos3Q

Please explain. I do not know how to do this. Thank You!!

  • Math -

    if Q = pi/2 + h
    r = 16 cos (3pi/2 +3h)
    = 16[ cos 3pi/2 cos 3h - sin 3pi/2 sin h ]
    cos 3pi/2 = 0
    sin 3pi/2 = -1
    so
    16 sin h
    is it the same for -h?
    if Q = pi/2 - h
    r = 16 cos (3 pi/2 -3h)
    =16[ cos 3pi/2 cos 3h + sin3 pi/2 sin 3h
    =16 (-sin h)
    sin h is not the same as -sin h
    so no, not symmetric about 3pi/2

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