i have a ti 83, and i want to plug this equation r=1+cos(theta)( this is polar coordinates) into my calculator but the graph does not look right. i think i messed around with the windows or table set menu and i cant fix it. can someone tell me what numbers i should put in my windows menu and table set.
To graph the polar equation r=1+cos(θ) on a TI-83 calculator, you need to make sure that the window and table set settings are appropriate for your equation. Here's how to do it:
1. Access the "Window" menu by pressing the "WINDOW" button on your TI-83 calculator.
2. Set the values for the X (θ) and Y (r) ranges. Since cosine varies from -1 to 1, it's a good idea to set the X range to cover a full period of the cosine function, like 0 to 2π. For example, you can set the X range as follows:
- Xmin (θ min): 0
- Xmax (θ max): 6.28 (corresponding to 2π)
3. Set the values for the Y (r) range. Since the r-value can be positive or negative depending on the angle θ, it's good to set a symmetrical Y range to include all possible values. For example, you can set the Y range as follows:
- Ymin (r min): -1
- Ymax (r max): 2
4. Determine the values for the Xscl (θ scale) and Yscl (r scale). These settings control how many units are displayed on each axis. Good starting values for the X and Y scales are 1.
5. Once you have set up the window, exit the "Window" menu.
6. Access the "Table Set" menu by pressing the "2nd" button, followed by the "TABLE SET" button.
7. Set the independent variable (θ) values for the table. For example, you can set the TblStart value as follows:
- TblStart: 0 (corresponding to Xmin)
8. Set the ΔTbl value, which determines the interval between the θ values in the table. For example, you can set the ΔTbl value as follows:
- ΔTbl: 0.1 (or any value you prefer)
9. Once you have set up the table settings, exit the "Table Set" menu.
10. You should now be able to graph the polar equation r=1+cos(θ) accurately on your TI-83 calculator. Move to the graphing screen and press the "GRAPH" button to see the plot.
By following these steps, you can make sure that the window and table set settings are appropriate for your equation, allowing you to visualize the graph accurately.