4 1. In Theorem 5.3.1 D, if 0= 5,5, II find T 6 3 -4 Theorem...

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4 1. In Theorem 5.3.1 D, if 0= 5,5, II find T 6 3 -4 Theorem 5.3.1. Let T: R? → R² be the orthogonal projection on a line I passing through the origin (0, 0) and let the angle between I and the x-axis be 0 (see Figure 5.3 O). Then (5.3.1) r(")-(cos@sine ") (;) cos²0 sin 0 cos 0 sin'o ):). Proof From Figure 5.3 D, we see that (5.3.2) (w1, w2) = (r cos 0,r sin 0). We prove the following assertion. (5.3.3) r = x cos 0 +y sin 0. Indeed, by Figure 5.3 D, r = s cos B= s cos(0 - a) and Figure 5.3: Reflection operator B(w1, w2) w2 A(x, y) Wi C D 4 1. In Theorem 5.3.1 D, if 0= 5,5, II find T 6 3 -4 Theorem 5.3.1. Let T: R? → R² be the orthogonal projection on a line I passing through the origin (0, 0) and let the angle between I and the x-axis be 0 (see Figure 5.3 O). Then (5.3.1) r(")-(cos@sine ") (;) cos²0 sin 0 cos 0 sin'o ):). Proof From Figure 5.3 D, we see that (5.3.2) (w1, w2) = (r cos 0,r sin 0). We prove the following assertion. (5.3.3) r = x cos 0 +y sin 0. Indeed, by Figure 5.3 D, r = s cos B= s cos(0 - a) and Figure 5.3: Reflection operator B(w1, w2) w2 A(x, y) Wi C D