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The point P rotates with angle α to point P'. the coordinates of the old P are x_{1} and x_{2} and for P': x'_{1} and x'_{2}.
Prove that:
$$x'_1=x_1\cos\alpha+x_2\sin\alpha$$
$$x'_2=x_2\cos\alphax_1\cos\alpha$$
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.
Prove that:
$$x'_1=x_1\cos\alpha+x_2\sin\alpha$$
$$x'_2=x_2\cos\alphax_1\cos\alpha$$
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.
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