## 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.

More later,

Nalin Pithwa

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