A bike is ridden at constant speed so that the wheel which has radius 30 cm makes 4 revolutions every second. Let y be the height above the road of a speck of paint on the outside of the tire. Find an equation for y at any time t for each of the initial conditions given below. Make good use of graphs to illustrate your solution. (a) at t= 0 the speck is 30 cm above the road (level with the axle) and moving up. (b) at t= 0 the speck is 60 cm above the road (at the top of the tire). In this case give two different answers using both the sine and the cosine functions. (c) at t= 0 the speck is 45 cm above the road and moving up. Use the sine function. (d) at t = 0 the speck is sitting on the road.

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