# ImplicitRegion fails on apparently simple case

Consider the shaded region bounded by $$sin x$$, $$cos x$$, and $$tan x$$:

We can define this as an `ImplicitRegion` by:

``````(ScriptCapitalR) =
ImplicitRegion((0 < x < 1) (And) (y < Cos(x)) (And)
(y < Tan(x)) (And) (y > Sin(x)),
{x, y})
``````

However, `RegionPlot((ScriptCapitalR))` fails to yield a figure after 15 minutes (v 11.3, MacOS).

However if I’m “smart” and put the bounds as $$0 I do get a plot.

Moreover, its area,

``````RegionMeasure((ScriptCapitalR))
``````

does not give an analytic solution (even after `RootReduce`, `Simplify`, etc.) even though an analytic form exists.

(One can get a numerical value through `N@RegionMeasure((ScriptCapitalR))`, but I seek the analytic solution.)

I’ve tried various forms based on `RegionIntersection()` and such, without success.

Of course I can use traditional calculus through `Integrate` and finding intersection points, but I’d like to compute the area more directly.

How can I 1) plot the region and (more importantly) 2) compute the analytic area?