document.write( "Question 1080745: Graph the following polar equation of r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π\r
\n" ); document.write( "\n" ); document.write( " $\"n+=+-5+\"$ to $\"+n+=+5+\"$ should transfer shaped from a heart to a bell. Which values of $\"+n+\"$ produce this heart-shaped curve and which values of $\"n\"$ produce the bell-shaped counter-part? \n" ); document.write( "

Algebra.Com's Answer #694887 by jim_thompson5910(35256) $\"\"$ $\"About$

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Below is the animation depicting all eleven graphs shown one at a time. Please be patient to let the animation load and cycle through. \r
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\n" ); document.write( "\n" ); document.write( "Take note of the slider up at the top right. As the slider moves, the equation and corresponding graph changes.
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\n" ); document.write( "Images and gif generated by GeoGebra (free graphing software).\r
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\n" ); document.write( "\n" ); document.write( "The heart shape occurs when n = -4 or n = -5 while the bell shape happens when n = 4 or n = 5. So it appears that the two shapes occur at the opposite ends of this interval [-5, 5]. \n" ); document.write( "

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