Use a graphing utility to graph the polar equation shown below.
r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π
For the integers n = -5 to n = 5. As you graph these equations, you should see the graph change shape from a heart to a bell.
I'm sorry. I'm having issues with graphing this.
try this site:
http://www.wolframalpha.com/input/?i=plot+r+%3D+cos+5%CE%98+%2B+n+cos+%CE%98,+0+%E2%89%A4+%CE%98+%E2%89%A4+%CF%80,+n%3D1
No problem! I can guide you through the process of graphing this polar equation using a graphing utility. For this particular polar equation, it might be easiest to use a graphing software or calculator that supports polar graphs. Here's a step-by-step approach:
1. Open the graphing utility or software that supports polar graphing. Some popular options include Desmos, GeoGebra, or WolframAlpha.
2. Set the graphing mode to polar coordinates. This will allow you to enter and visualize polar equations.
3. Enter the equation: r = cos(5θ) + n * cos(θ).
- Make sure to include the parentheses around the angles (θ) and the multiplication symbol (*) before the "cos" term.
- Also, replace "n" with the integers from -5 to 5, one value at a time. This will allow you to graph each equation separately and observe how the graph changes.
4. Set the range for the angle: 0 ≤ θ ≤ π. This will restrict the graph to the interval from 0 to π radians.
5. Plot the graph for each value of "n" as a separate curve or trace.
- Start with n = -5 and plot the corresponding graph.
- Then, increment the value of "n" by 1 and plot the graph again, repeating this process until you reach n = 5.
- This will allow you to observe the shape transformation from a heart to a bell as you go from n = -5 to n = 5.
By following these steps, you should be able to graph the polar equation and observe how the graph changes shape. If you encounter any specific issues or error messages, please let me know, and I'll be happy to help troubleshoot!