Graphs of trig raised to trig

Question: Consider the function

y=f(x)=x^{x}. Can you graph it? It is variable raised to variable. Send me your observations.

Now, consider the functions:

(\tan \theta)^{\tan \theta}, (\tan \theta)^{\cot \theta},

(\cot \theta)^{\tan {\theta}}, (\cot \theta)^{\cot \theta}.

Can you graph these? What is the difference between these and the earlier generalized case?

Now, consider the function:

Let 0 \deg < \theta < 45 \deg.

Arrange t_{1}=(\tan \theta)^{\tan \theta}, t_{2}=(\tan \theta)^{\cot \theta}

t_{3}=(\cot \theta)^{\tan \theta} and t_{4}=(\cot \theta)^{\cot \theta}

in decreasing order.

Kindly send your comments/observations.

More later,

Nalin Pithwa

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