refer to the following: The sword artistry of the Samurai

Chapter 8, Problem 70

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refer to the following: The sword artistry of the Samurai is legendary in Japanese folklore and myth. The elegance with which a samurai could wield a sword rivals the grace exhibited by modern gure skaters. In more modern times, such legends have been rendered digitally in many different video games (e.g., Onimusha). In order to make the characters realistically move across the screen, and in particular, wield various sword motions true to the legends, trigonometric functions are extensively used in constructing the underlying graphics module. One famous movement is a gure eight, swept out with two hands on the sword. The actual path of the tip of the blade as the movement progresses in this gure-eight motion depends essentially on the length L of the sword and the speed with which it is swept out. Such a path is modeled using a polar equation of the formwhose graphs are called lemniscates. r2(u) = L cos(Au) or r2(u) = L sin(Au), u1. Video Games. Write a polar equation that would describe the motion of a sword 12 units long that makes 8 complete motions in