- #1

Karol

- 1,380

- 22

The point P rotates with angle α to point P'. the coordinates of the old P are x

Prove that:

$$x'_1=x_1\cos\alpha+x_2\sin\alpha$$

$$x'_2=x_2\cos\alpha-x_1\cos\alpha$$

I drew on the left the problem and on the right my attempt. the line OA, which is made of ##x_1\cos\alpha## plus ##x_2\sin\alpha## which is the blue line is indeed x'

_{1}and x_{2}and for P': x'_{1}and x'_{2}.Prove that:

$$x'_1=x_1\cos\alpha+x_2\sin\alpha$$

$$x'_2=x_2\cos\alpha-x_1\cos\alpha$$

I drew on the left the problem and on the right my attempt. the line OA, which is made of ##x_1\cos\alpha## plus ##x_2\sin\alpha## which is the blue line is indeed x'

_{1}but i don't see the congruent triangles.