a) Take the point in the plane (one unit right on the x-axis). Explain why rotating this point 0 radians counter-clockwise gives the point cos 0 sin 0 b) Take the point E in the plane (one unit up on the y-axis). Explain why rotating this point 0 radians counter-clockwise gives the point cos(0 + TT/2) sin(0 + 7/2) . Some high-school trig shows that this is equal to c) In the previous two parts, you showed that Po (b) - (8:8). - sin 0 Ro = cos 0 Use the assumption that Re is linear to show that x cos 0 - y sin 0 Re x sin 0 + y cos 0Hints 5. For (a)+(b): The whole point of the functions cos 6 and sin 6 are that (cos 6, sin 6) are the (9:, y)-coordinates of the point on the unit circle 6 radians counter-clockwise from (1, 0). For (c): you need to use both of the axioms of linearity