Problem:
Using the TI-85 graphing calculator, find the coordinates of the two points of intersection of the graphs of

f(x) = 3 sin(x)
and
g(x) = x2 + 1

Visualization:

[Press here to see animation again!]

1. If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
2. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
3. If necessary, keep pressing F4 key until only y1= appears on the screen.
4. At the prompt y1=, type in

3 sin x

and press the ENTER key.

5. At the prompt y2=, type in

x^2 + 1

and press the ENTER key.

6. The range settings for the graph above is  [-pp] × [-3, 5]:

7. Pick GRAPH by pressing the F5 key.
8. Press the MORE key so that MATH appears on the menu.
9. Press the F1 key to pick MATH.
10. Again, press the MORE key so that ISECT appears on the menu.
11. Pick ISECT by pressing the F5 key.
12. You will now see a flashing star at the origin and the coordinates of the at the bottom of the screen:

13. Using the right and left arrow keys, move the star as close as possible to one of the two points of intersection of the two graphs and press the ENTER key.
14. The star now moves to the second graph.
15. Press the ENTER key again and you will then see the coordinates of the first point of intersection:

16. Press the EXIT key followed by the F5 key to pick ISECT again.
17. Again, using the right and left arrow keys, move the star as close as possible to the second point of intersection and press the ENTER key twice. You will then see the coordinates of the second point of intersection: