[tex]\bf \textit{symmetry test with respect to the }\theta =\frac{\pi }{2}~line
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r=4cos(2\theta )\implies r=4cos[2(\pi -\theta )]\implies r=4cos(2\pi -2\theta )\\\\
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[tex]\bf cos(2\pi -2\theta )\implies \stackrel{1}{cos(2\pi )}cos(2\theta )+\stackrel{0}{sin(2\pi )}\stackrel{}{sin(2\theta )
}
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1\cdot cos(2\theta )+0\cdot sin(2\theta )\implies cos(2\theta )+0\implies cos(2\theta )\\\\
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r=4cos(2\theta )\impliedby \textit{is symmetric with respect to }\theta =\frac{\pi }{2}~line[/tex]
