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sin1309X=1140X, Can it be solved?
Rank: Newbie
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Joined: 14/06/2009(UTC) Posts: 2 Location: India
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subjected Equation is detailed as under: In a Circle if S is arc length, L is chord length and R is Radius and 'Theta' is angle of arc subtented at centre of circle in radians. then by geometry S = 'R'.'Theta', where Theta in radians and R is Radius. or Theta/2 = S/2R -----Eq 1 and also in triangle made by R , L/2 and base from centre to one end of L/2 Sin (Theta/2) = L/2R ----Eq 2 thus from Eq 1 and 2 Sin (S/2R) = L/2R if an Arc length 'S' is given = 2618. its chord length 'L' is also given = 2280. then equation will be Sin (1309X) = 1140X, Where X =1/R Edited by user 14 June 2009 20:02:47(UTC)
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Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)
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The result iz zero (see the example of finding roots). Try, for instance, function solve and solve the equation sin(1.309*x)-1.140*x (there should be three values)
By the way, if we try to plot the function sin(1309*x)-1140*x and zoom in, we are going to see very small numbers with the 15 significant digits on the axis ticks, say x.xxxxxxxxxxxxxxE-xx. This is rather hard to read especially on the x axis. I suppose that there should be used the same number of decimal places as defined under Tools=>Options=>Decimal places, or something else?
Regards, Radovan |
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!" |
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Rank: Newbie
Groups: Registered
Joined: 14/06/2009(UTC) Posts: 2 Location: India
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omorr wrote:The result iz zero (see the example of finding roots). Try, for instance, function solve and solve the equation sin(1.309*x)-1.140*x (there should be three values)
By the way, if we try to plot the function sin(1309*x)-1140*x and zoom in, we are going to see very small numbers with the 15 significant digits on the axis ticks, say x.xxxxxxxxxxxxxxE-xx. This is rather hard to read especially on the x axis. I suppose that there should be used the same number of decimal places as defined under Tools=>Options=>Decimal places, or something else?
Regards, Radovan Dear Frnds Actually in excel, values can easily be brought out by using Goal seek option. I am pasting here the same: Radius Excel Formula and value C9 - value = cos(1309/C9)-((C9-525)/C9) 1534.578119 -0.000162479 Here I put a additional formula: sin(1309/R) - L/2R =0. Radius C7 value Excel Formulae and value =SIN(1309/C7)-(1140/C7) 1455.558167 -0.000306041 Next: Solution of sin(X ) or cos(X ) or other trigonometric functions could only be solved in form of expansion of series. So in place of sinaX or cosaX , that series can be replaced up to the required terms wrt the required decimal. But again it is a tedious due to multi power series Sin(X) = X – (X^3)/3! + (X^5)/5! – (X^7)/7! + ---- -------- ------- Cos (X) = 1 – (X^2)/2! + (X^4)/4! – (X^6)/6! + ----- ----- ----
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Rank: Advanced Member Groups: Registered
Joined: 24/10/2009(UTC) Posts: 52 Location: Denmark
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My TI 89 Titanium says 0 :P If anyone cares...
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Rank: Advanced Member Groups: Registered
Joined: 30/08/2009(UTC) Posts: 52 Location: Australia
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We have a maths problem, not an Smath problem. 0 is a correct answer. AFAIK there is no other.
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Rank: Newbie
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Joined: 18/12/2009(UTC) Posts: 1 Location: Tennessee, USA
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I solve using OpenOffice Spreadsheet (Goal Seek)and I get R = 1457.555. Zero is not the only answer, I believe.
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Rank: Administration Groups: Registered, Advanced Member Joined: 23/06/2009(UTC) Posts: 1,740 Was thanked: 318 time(s) in 268 post(s)
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Here it is, again Regards, Radovan |
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!" |
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sin1309X=1140X, Can it be solved?
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