A piston is designed as follows: One metal rod of length one is fixed to a crank at the origin, and the other end rotates in a circle of radius 1. Let the other end of this metal rod be the (variable) point A. A second rod is attached at A, with its other end able to slide back and forth along the positive side of the x-axis. Call this point B, so that B will always have a y-coordinate of 0. Let the distance from A to B = 3, that is, the second metal rod has length 3. Let = the angle the first rod makes with the positive side of the x-axis.For each question, explain in words how you would find the coordinates. Do not give the direct answer, just explain how you would solve the problem.

1. If = 90 , what is the coordinates of A

2. If = 60 , what is the coordinates of A

3. If = 30 , what is the coordinates of A

4. If = 90 , what is the coordinates of B

5. If = 60 , what is the coordinates of B

6. If = 30 , what is the coordinates of B

7. For an arbitrary angle , what is the coordinates of A

8. For an arbitrary angle , what is the coordinates of B