A metal rod 1 meter in length is placed horizontally on the x-axis, with its ends located at the points P = (0,0) and Q = (1,0). A second long metal rod is attached to the first one at the point Q =(1,0) and makes an angle of 45 with the first. A third long metal rod is attached to the rst rod at the point P =(0,0) and is free to rotate about P. Thus, the angle 6 made by the rst and third bars is free to change. For 6 between 0 and 90 the second and third bars cross at a point R=(x,y) (see figure). 9 450 P Q (a) Find a relationship between x, y and 9; then eliminate y by expressing y in terms ofx. This gives you a relationship between x and 6 of the form: (Write theta to represent 6.) x tan(6l) = 1-x. J (b) Notice that x=0.5 meter when 0 = 45". By approximately how many radians should you increase 6 if you want the x coordinate of the point R to decrease to x = 0.45 meters? Use the tangent line approximation