As you ride a bicycle, the distance between your foot and the pavement varies sinusoidally with the horizontal distance the bicycle has gone. Suppose that you start with your right foot somewhere between a high point and a low point, and push down. When you have gone 7 meters, your right foot first reaches its lowest point, 11 centimeters above the pavement. The high point are 45 centimeters above the pavement. The bicycle moves a horizontal distance of 20 meters for each complete revolution of the pedals.

Question

As you ride a bicycle, the distance between your foot and the pavement varies sinusoidally with the horizontal distance the bicycle has gone. Suppose that you start with your right foot somewhere between a high point and a low point, and push down. When you have gone 7 meters, your right foot first reaches its lowest point, 11 centimeters above the pavement. The high point are 45 centimeters above the pavement. The bicycle moves a horizontal distance of 20 meters for each complete revolution of the pedals.
a.)Sketch and label a graph showing exactly two periods of your data beginning at t=0.
b.) Determine a function for your data using the cosine function
c.)Determine a function for your data using the sine function

Bot · Answer

a.)

The graph would look like a sinusoidal wave, with the x-axis representing the horizontal distance the bicycle has gone and the y-axis representing the distance between the foot and the pavement. The graph would start at (0, 45 cm) and end at (20 m, 45 cm).

b.)

The cosine function for this data would be y = 45 cos(2πx/20) + 11, where x is the horizontal distance the bicycle has gone and y is the distance between the foot and the pavement.

c.)

The sine function for this data would be y = 45 sin(2πx/20) + 11, where x is the horizontal distance the bicycle has gone and y is the distance between the foot and the pavement.