SOLUTION: Graph the following polar equation of r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π {{{n = -5 }}} to {{{ n = 5 }}} should transfer shaped from a heart to a bel

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Question 1080745: Graph the following polar equation of r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π
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?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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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.

Take note of the slider up at the top right. As the slider moves, the equation and corresponding graph changes.

Images and gif generated by GeoGebra (free graphing software).


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].