Consider Example 6 on page A30 in the Stewart text: "Find all values of x in the interval such that sin x = sin 2x." The result of entering this function into the TI-89's solve function as "solve(sin(x)=sin(2x),x)" is shown at right. (You can get the solve function by pressing and selecting "1: solve(" or by typing the letters). The calculator has delivered several solutions ( the right-pointing arrow on the solution line indicates that there are more solutions on the line), but they are approximations. This may or may not be good enough. |
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In order to help the TI-89 find exact solutions, we can follow the lead of Example 6 and realize that sin 2x = 2 sin x cos x, which reduces all of the functions to the same argument. Entering "solve(sin(x)=2sin(x)cos(x),x)" produces the result shown at right. Well, the good news is that the TI-89 has produced exact solutions for this version of the equation. The bad news is that you probably have no idea what they are. Here's the deal: In the expression , @n1 represents an integer, so, solutions indicated by this expression are: (Notice that only one of these solutions is in the domain of the problem.) In this way, you can find all of the solutions that fall in the interval . |
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Is there an easier way? Yes, sometimes. The screen shot at right shows what happens when you specify the domain of solution to the solve command. Here, adding gives the 5 solutions in the interval in easily-readable form. Hooray! Note: You get the "greater than or equal" sign by pressing (instead of ), and you can get "and" from or by typing the letters. |
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