Part 3/7:
The trigonometric functions used play a crucial role in creating the heart shape. For instance, examining the cosine function alone, we understand that it oscillates. The equation incorporates a cosine term that has been modified by multiplying by a rapidly oscillating factor of (400x). This adjustment to the cosine function means that the period is compressed, resulting in much quicker oscillations which help build the intricacy of the heart shape:
- Period of Cosine: In a standard cosine function, the period is (2\pi). However, for the term (\cos(400x)), the new period becomes (\frac{\pi}{200}), meaning the function oscillates more frequently.
The interplay of the cosine functions contributes to the up-and-down movement characteristic of the heart shape.