n n Curves of the form x = = cos(t) + 1cos((n = 1)t), y =...

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n n Curves of the form x = "=¹ cos(t) + 1cos((n = 1)t), y = n=¹ sin(t) + sin((n-1)t) are called hypocycloids. Plot the following three curves on the same axes. Use different colors to identify different curves. i. x = cos(t) + 1cos(3t), y = sin(t) + ii. x = cos(t)+cos(4t), y = sin(t) + cos(t)+cos (5t), y = sin(t)+ sin(5t), (with n = 6) Based on your graphs, what happens as we change n? What stays the same? = sin(3t), (with n = 4) sin(4t), (with n = = 5) n n Curves of the form x = "=¹ cos(t) + 1cos((n = 1)t), y = n=¹ sin(t) + sin((n-1)t) are called hypocycloids. Plot the following three curves on the same axes. Use different colors to identify different curves. i. x = cos(t) + 1cos(3t), y = sin(t) + ii. x = cos(t)+cos(4t), y = sin(t) + cos(t)+cos (5t), y = sin(t)+ sin(5t), (with n = 6) Based on your graphs, what happens as we change n? What stays the same? = sin(3t), (with n = 4) sin(4t), (with n = = 5)