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I'm trying to find the intersection points of the following plot with the given boundaries. How would I do so in the bounds set by the above plot? I've tried FindRoot by setting the lines equal to each other and doing {t,0} but my program won't load in a result. 

Plot[{(2000/ 5280 E^(-1.21 ((2.5 + 1.5 Cos[Pi/3 t] - 1)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 3.5)^2))) + (2000/ 5280 E^(-4 ((2.5 + 1.5 Cos[Pi/3 t] - 4.5)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 1.5)^2))) + (-950/ 5280 E^(-1 ((2.5 + 1.5 Cos[Pi/3 t] - 2.8)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 3.7)^2))) + (1000/( 5280 (1 + 2.25 ((2.5 + 1.5 Cos[Pi/3 t] - 2.5)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 1.8)^2)))) + (1500/( 5280 (1 + 1.21 ((2.5 + 1.5 Cos[Pi/3 t] - 3)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 2)^2)))) + (3500/( 5280 Sqrt[ 1 + 3.61 ((2.5 + 1.5 Cos[Pi/3 t] - 1)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 1)^2)])) + (2000/( 5280 Sqrt[ 1 + 4 ((2.5 + 1.5 Cos[Pi/3 t] - 4.25)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 4.1)^2)])) + (200/5280 Sqrt[ 1 + .25 ((2.5 + 1.5 Cos[Pi/3 t] - 2.75)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 3.75)^2)]) + 7000/5280, 1.893939}, {t, 0, 6}]
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  • $\begingroup$ The methods in the linked question are all usable for your specific case. $\endgroup$ Commented Nov 15, 2019 at 2:59

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expr = (2000/ 5280 E^(-1.21 ((2.5 + 1.5 Cos[Pi/3 t] - 1)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 3.5)^2))) + (2000/ 5280 E^(-4 ((2.5 + 1.5 Cos[Pi/3 t] - 4.5)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 1.5)^2))) + (-950/ 5280 E^(-1 ((2.5 + 1.5 Cos[Pi/3 t] - 2.8)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 3.7)^2))) + (1000/(5280 (1 + 2.25 ((2.5 + 1.5 Cos[Pi/3 t] - 2.5)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 1.8)^2)))) + (1500/(5280 (1 + 1.21 ((2.5 + 1.5 Cos[Pi/3 t] - 3)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 2)^2)))) + (3500/(5280 Sqrt[ 1 + 3.61 ((2.5 + 1.5 Cos[Pi/3 t] - 1)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 1)^2)])) + (2000/(5280 Sqrt[ 1 + 4 ((2.5 + 1.5 Cos[Pi/3 t] - 4.25)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 4.1)^2)])) + (200/5280 Sqrt[ 1 + .25 ((2.5 + 1.5 Cos[Pi/3 t] - 2.75)^2 + (2.4 + 1.1 Sin[Pi/3 t] - 3.75)^2)]) + 7000/5280 roots = NSolve[expr == 1.893939 && 0 < t < 6, t]

gives roots:

{{t -> 2.20967}, {t -> 2.63666}, {t -> 3.52713}, {t -> 4.85185}}

And we can visualize them:

Plot[expr, {t, 0, 6}, Frame -> True, Mesh -> {{1.893939}}, MeshFunctions -> (#2 &), MeshStyle -> Directive[PointSize[Medium], Red], GridLines -> {t /. roots, {1.893939}}, GridLinesStyle -> {Directive[Gray, Dashed], Directive[Thick, ColorData[97][2]]}]

enter image description here

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  • $\begingroup$ Thank you so much! $\endgroup$ Commented Nov 15, 2019 at 2:11
  • $\begingroup$ You are welcome! $\endgroup$ Commented Nov 15, 2019 at 2:47

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