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Answered 2011-12-14 03:50:20

The problem x = 2 sin x cannot be solved by using algebraic methods.

One solution is to draw the graphs of y = x and y = 2 sin x.

The two lines will intersect. The values of x where the intersection takes place are the solutions to this problem.

You can tell from the graph that one solution is x=0 and verify this contention by noting that 2 sin(0) = 0.

You can find the other solution through numerical methods and there are many that will give you the correct solution. Perhaps the simplest is to start with a value of X like pi/2 and then take the average of 2*sin(X) and X. Using that as your new value, again take the average of 2*sin(X) and X. As you continue to do this, the value will get closer and closer to the desired value. After 20 steps or so, the precision of your calculator will probably be reached and you will have a pretty good answer of about 1.89549426703398. (A spreadsheet can be used to make these calculations pretty easily.)

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