More Positions on the Ferris Wheel Part I: Clockwise and Counterclockwise The two Ferris wheel riders shown here both started from the 3 o'clock position. The rst rider turned 30" and is now at the 2 o'clock position. The second rider turned 30 and is now at the 4 o'clock position. Negative angles, you'll recall, are interpreted as clockwise motion. Assume the radius of the Ferris wheel is 50 feet. Recall that if a rider turns through an angle 6, then his x-coordinate is given by the expression 50 cos 9. Therefore, the rst rider's x-ooordinate is 50 cos 30 and the second rider's xcoordjnate is 50 cos (30). l. 3. Explain why these two riders have the same x-coordinate. That is, why are they the same distance to the right of the center of the Ferris wheel? b. What does your answer to part a tell you about cos 30 and cos (-30)? Now consider the general situation. In the next diagram. points C and D represent two positions on a Ferris wheel. In the case of point C, the rider has turned through an angle 9. For point D, the rider has turned through an angle 6. 2. a. Explain why points C and D have the same x-coordinate. C b. Use the diagram and your answer to part a to explain why cos B and cos (-6) must A x be equal. V Y 2. Set up and solve a quadratic equation to answer each of these questions. a. A rectangle with one side 5 feet longer than the other side has an area of 126 square feet. What are the rectangle's dimensions? b. A right triangle has one leg 6 inches shorter than the other leg, and its hypotenuse is 13 inches long. How long are the triangle's legs? c. An object is thrown up into the air from the roof of a building. Its height above the ground h (in feet) after t seconds is given by the equation h = 90 + 50t - 16t. When will the object be 120 feet high