Question

Describe in your own words how you find the coordinates for any point (x, y) when it is rotated 90 degrees counterclockwise about the origin.
Show a graph and an example of this type of rotation.

Answer 1

Answer:

Considering the point $(x, y)$

If you represent it as a complext number, you get:

- Counterclockwise if multiplying by $i$

- Clockwise if multiplying by $-i$

Note, I'm considering $x+iy$

Another approach using trigonometry is considering:

$(x,y)=(cos\theta,sin\theta)$

So the rotation will get the coordinates

$(cos\theta+\frac{\pi}{2} ,sin\theta+\frac{\pi}{2})$