What is theta value?

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Using a pre-defined formula in Desmos android app the following example is given :

enter image description here

What is value of theta used within formula for evaluating r ? Is it some implicit value, as it's value is not displayed.

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I believe you are plotting in polar coordinates, the two independent variables are $r$ and $\theta$. Hence the values of $\theta$ are from a range, $-\pi$ to $\pi$, or 0 to $2\pi$.

It is like $y=2x+1$, the value of $x$ takes all real numbers, not just a single value.