To graph the parametric equations given by x = 7 sin(t) sin(7t) and y = 7 cos(t) cos(7t), we can follow these steps:
- Understand the Variables: Here, t is the parameter that varies over some interval, typically 0 to 2π. The values of x and y will depend on how t changes.
- Calculate Points: We will evaluate the equations for various values of t within the interval. For instance, you might select t = 0, π/4, π/2, π, 3π/2, 2π to get a set of corresponding x and y coordinates.
- Plot the Points: After calculating several points, plot them on a Cartesian plane. Each point will represent a position of (x, y) for each corresponding value of t.
- Connect the Dots: Once you have plotted enough points, you can connect them smoothly to visualize the path traced out by the parametric equations. The shape you get will be periodic and can exhibit interesting features due to the sine and cosine functions.
By following these steps, you can effectively graph the given parametric equations and observe the unique patterns that emerge from the interaction of the sine and cosine functions.