give the answer of the transformations that need to happen to the original equation stated in the question. simply state the equation 

To transform the original parametric equations \(x(t) = \cos(t)\) and \(y(t) = \sin(t)\), different types of transformations can be applied. However, without specific instructions on the desired transformations from the image, I will provide a few common transformations:

1. **Translation**: To translate the circle by \(h\) units horizontally and \(k\) units vertically:
   \[
   x(t) = \cos(t) + h, \quad y(t) = \sin(t) + k
   \]

2. **Scaling**: To scale the circle by a factor of \(a\) horizontally and \(b\) vertically:
   \[
   x(t) = a\cos(t), \quad y(t) = b\sin(t)
   \]

3. **Rotation**: To rotate the circle by an angle \(\theta\) counterclockwise around the origin:
   \[
   x(t) = \cos(t)\cos(\theta) - \sin(t)\sin(\theta), \quad y(t) = \sin(t)\cos(\theta) + \cos(t)\sin(\theta)
   \]

If you have a specific transformation in mind, please let me know, and I can provide the exact equations.

Explore how to transform parametric equations x(t) = cos(t) and y(t) = sin(t) through translation, scaling, and rotation. Learn the equations for translating, scaling, and rotating parametric curves in 2D. Suitable for advanced high school students and beyond.

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