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Solve these trigonometric equations?


I tried to solve these two eqn by solve function and reduce , but it does not work . can anyone help me , please ??

eq1 = (1500 - 100/Sin[alp])/Sin[180 - alp - th2] == (1176.795 - 100/Tan[alp])/Sin[th2];`
eq2 = 200 Cos[90 - alp - th2] - 500 Sin[alp] == 100;
POSTED BY: Ahmed Khodari
10 months ago

Solve usually works best with polynomial problems. Reduce can often do better with trig problems.

Since you included 180 and 90 in your trig functions I assume you might be thinking in degrees rather than radians. So I inserted a couple of Degree. You may need to insert more of those is you are thinking some of your other constants are in degrees. When you get the solution you can then divide each of the numeric values by Degree to get from radians back to degrees. Look at Degree in the help system for more information.

Since you have two equations and two unknowns and trig functions there is more than one solution. Some of those additional solutions depend on multiples of pi and those multiples are indicated by unknown constants C[1] and C[2]. There are even some solutions involving complex numbers, which you might not be interested in.

eq1 = (1500 - 100/Sin[alp])/Sin[180 Degree - alp - th2] == (1176.795 - 100/Tan[alp])/Sin[th2];
eq2 = 200 Cos[90 Degree - alp - th2] - 500 Sin[alp] == 100;
Reduce[{eq1, eq2}, alp]
POSTED BY: Bill Simpson
10 months ago

Are your variables in radiants or degrees? If they are degrees, you had better write your equations this way:

eq1 = (1500 - 100/Sin[alp*Degree])/
    Sin[(180 - alp - th2) Degree] == (Rationalize[1176.795] - 
eq2 = 200 Cos[(90 - alp - th2)*Degree] - 500 Sin[alp*Degree] == 100;

These are trascendental equations, not very suitable for Solve. You can get a feeling for the solutions with a plot

ContourPlot[Evaluate[{eq1, eq2}], {alp, 0, 360}, {th2, 0, 360}]

I can see three probable solution. You can get better approximation with FindRoot

POSTED BY: Gianluca Gorni
10 months ago

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