How would I graph r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = -5 to n = 5. ?
To graph the equation r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π for the integers n = -5 to n = 5, you can follow these steps:
1. Plot a set of points for Θ ranging from 0 to π in small increments. For example, you can choose 50 values of Θ between 0 and π.
2. For each value of n in the range -5 to 5, calculate the corresponding value of r using the equation r = cos 5Θ + n cos Θ for each value of Θ.
3. Plot the calculated points (r, Θ) on a polar coordinate system, where the radial distance represents the value of r and the angle represents Θ.
4. Connect the plotted points for each value of n to form a curve.
5. Repeat steps 2-4 for each value of n in the range -5 to 5.
By following these steps, you will be able to graph the equation r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π for the given range of integers n = -5 to n = 5.