summarize the formulas for rotation of 90, 180 and 270 degrees counter clockwise
user
Sure, I'd be happy to help you understand the formulas for rotating a point in the plane. These formulas are commonly used in mathematics and computer graphics, but I'll present them in more general terms.

- **90-degree counterclockwise rotation**: This rotation is often denoted by the symbol "R90". The formula for this rotation is as follows:

  R90(x, y) = (y, -x)

  This means that the first coordinate (x) becomes the second coordinate (-y), and the second coordinate (y) becomes the first coordinate (-x). Essentially, you swap the x and y coordinates, and then flip the x coordinate.

- **180-degree counterclockwise rotation**: This rotation is often denoted by the symbol "R180". The formula for this rotation is:

  R180(x, y) = (-x, -y)

  This means that both coordinates are flipped, resulting in a reflection across the origin.

- **270-degree counterclockwise rotation**: This rotation is often denoted by the symbol "R270". The formula for this rotation is:

  R270(x, y) = (-y, x)

  This means that the x coordinate becomes the second coordinate (-y), and the y coordinate becomes the first coordinate (x). Essentially, you swap the x and y coordinates, and then flip the y coordinate.

These formulas can be useful for performing certain kinds of geometric transformations. However, be aware that they are not useful for all types of rotations, such as rotations around the z-axis, which are platyular in nature. In those cases, more advanced mathematics like matrix operations might be used.
assistant
summarize the formulas for rotation of 90, 180 and 270 degrees counter clockwise
user
Sure, I'd be happy to help with that! Here are the formulas for rotating a point (x, y) in a 2D plane:

1. **90 degrees counterclockwise rotation**:
   The new coordinates (x', y') can be calculated using the following formulas:
   x' = -y
   y' = x

2. **180 degrees counterclockwise rotation**:
   The new coordinates (x', y') can be calculated using the following formulas:
   x' = -x
   y' = -y

3. **270 degrees counterclockwise rotation**:
   The new coordinates (x', y') can be calculated using the following formulas:
   x' = y
   y' = -x

These formulas are derived from the general rotation formula, which involves trigonometry, but for these specific angles, the sine and cosine values simplify to 0, 1, or -1.
assistant