Texas Instruments TI-82 User Manual - Page 201
Solving a System of Nonlinear Equations
UPC - 033317086337
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Solving a System of Nonlinear Equations Solve the equation X3-2X=2cosX graphically. Stated another way, solve the system of two equations and two unknowns: Y=X3-2X and Y=2cosX. Use the ZOOM factors to control the decimal places displayed on the graph. Procedure 1. Press z. Select the default MODE settings. Press y [STAT PLOT] and turn off all stat plots. Press o. Turn off all functions and enter the functions Y7=X3-2X and Y8=2cos X. 2. Press q and select ZDecimal. The display shows that there are two areas that might contain solutions (points where the two functions appear to intersect). 3. Press q ~ and select SetFactors... from the ZOOM MEMORY menu. Set XFact=10 and YFact=10. 4. Press q 2 (to select Zoom In). Use ~, |, }, and † to position the free-moving cursor on the apparent intersection of the functions on the right side of the display. As you move the cursor, note that the X and Y coordinates have one decimal place. 5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, note that now the X and Y coordinates have two decimal places. 6. Press Í to zoom in again. Move the free-moving cursor to a point exactly on the intersection. Note the number of decimal places. 7. Press y ãCALCä and select intersect. Press Í to select the First curve and Í to select the Second curve. Now trace to a Guess near the intersection and press Í. What are the coordinates of the intersection? 8. Press q and select ZDecimal to redisplay the original graph. 9. Press q. Select Zoom In and explore as above the other apparent intersection. Applications 14-7