13 rotated 50 degrees clockwise

Answer 1

To find the new position of the point after rotating it 50 degrees clockwise, we need to use the following formula:

(x', y') = (x \cdot \cos(\theta) + y \cdot \sin(\theta), -x \cdot \sin(\theta) + y \cdot \cos(\theta))

Let's assume the original position of the point is (x, y) = (1, 3).

Using the formula above, we can calculate the new position:

(x', y') = (1 \cdot \cos(50) + 3 \cdot \sin(50), -1 \cdot \sin(50) + 3 \cdot \cos(50)).

Calculating the values:

(x', y') ≈ (1 \cdot 0.64278761 + 3 \cdot 0.76604444, -1 \cdot 0.76604444 + 3 \cdot 0.64278761)
(x', y') ≈ (0.64278761 + 2.29813332, -0.76604444 + 1.92836283)
(x', y') ≈ (2.94092093, 1.16231839).

Therefore, after rotating 13 by 50 degrees clockwise, its new position is approximately (2.94092093, 1.16231839).