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Sine Oval and Nested Trig Functions

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nested function
sine oval
sin
cos
tan
csc
sec
cot
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scaled to fit
nesting
3
The unit circle is the set of all points
(x,y)=(cos(t),sin(t))
, but nesting the sine function in this formula,
(x,y)=(cos(t),sin(sin(sin(…sin(t)))))
, gives the sine oval, which becomes progressively more squarish with increased levels of nesting (controlled by the slider). Change the graph to "sin" to examine the nested sine function alone, whose squarish behavior is not shared by the other trig functions.
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