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How to find the interval where the root exists?

I've got a program which plots 2 graphs(Sin[x] and Log[y]) and 2 lists of rectangles(built from lists of numbers spx,spy) in accordance. Prompt, please, how to get the interval (or even the rectangle) andwhere these rectangles overlap?

spx = {-1, -0.75, -0.5 , -0.35, -0.25 , 0, 0.3, 0.775 , 0.95 , 1.55 , 
   1.6, 2.325 , 2.375 , 3.1, 3.825, 3.925, 4.55 , 4.7, 5.275 , 5.35, 
   5.675 , 6};
spy = {1, 2.25, 3.5, 4.75, 6}
g1 = Graphics[{EdgeForm[{Black, Thick}], {Pink, Opacity[0.7], 
     Table[Rectangle[{spx[[i]], 
        Sin[spx[[i]]] + Cos[spx[[i]]]}, {spx[[i + 1]], 
        Sin[spx[[i + 1]]] + Cos[spx[[i + 1]]]}], {i, 1, 
       Length[spx] - 1}]}}, Axes -> True];
g2 = Plot[{Sin[x]}, {x, -1, 6}, PlotStyle -> Thick];
g3 = Graphics[{EdgeForm[{Black, Thick}], {Yellow, Opacity[0.7], 
     Table[Rectangle[{spy[[i]], Log[spy[[i]]]}, {spy[[i + 1]], 
        Log[spy[[i + 1]]]}], {i, 1, Length[spy] - 1}]}}, Axes -> True];
g4 = Plot[{Log[y]}, {y, 1, 6}, PlotStyle -> Thick];
lift = {{x_Real, y_Real} :> {z, y, x}, Rectangle :> Cuboid};
lifted1 = N[g1] /. lift;
lifted2 = N[g2] /. lift;
lifted3 = N[g3] /. lift;
lifted4 = N[g4] /. lift;

zlevelI = 0;
zlevel[] := (zlevelI = zlevelI + .001);

Show[Graphics3D @@ (lifted1 /. z :> 0), 
 Graphics3D @@ (lifted2 /. z :> 1 + zlevel[]), 
 Graphics3D @@ (lifted3 /. z :> 0), 
 Graphics3D @@ (lifted4 /. z :> 1 + zlevel[])]![enter image description here][1]
POSTED BY: Julia Ilkiv
3 Replies
Posted 9 years ago
POSTED BY: Bill Simpson

It appears you use Log[y] rather than Cos[y]? Anyway, intersection points can be found with Solve.

Solve[Sin[x] == Log[x] && -1 <= x <= 6, x]

(* Out[75]= {{x -> 
   Root[{Log[#1] - 2 Tan[#1/2] + Log[#1] Tan[#1/2]^2 &,  2.2191071489137460325958}]}} *)
POSTED BY: Daniel Lichtblau

oh,it was a mechanical error) Thanks, but I need an interval or coordinates of rectangle, where these rectangles overlap. how to find it? out

POSTED BY: Julia Ilkiv
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