Question

As part of video game, the point (4,6) is rotated counterclockwise about the origin through an angle of 15 degrees. Find the new coordinates of this point

Answer 1

Answer:

  (2.31079, 6.83083)

Step-by-step explanation:

The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

Here, that means the new coordinates are ...

  (4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)