1. **State the problem:** We analyze the height $h(x)$ of a bike pedal above the crank arm's horizontal position as a function of the rotational angle $x$ in degrees. 2. **Identify period, amplitude, and axis:** - The period is the length of one full cycle of the sine wave. Given the graph and problem, the period is $360^\circ$ (one full rotation). - The amplitude is the maximum height from the midline to the peak, which is $13$ cm. - The axis (midline) is the horizontal line about which the sine wave oscillates, here $y=0$ cm. 3. **Interpretation:** - Period $360^\circ$ means the crank arm completes one full rotation every $360^\circ$. - Amplitude $13$ cm represents the radius of the circular path of the pedal. - Axis $y=0$ means the pedal height oscillates equally above and below the crank arm's horizontal position. 4. **Position of the handle when rotation began:** - At $x=0^\circ$, the graph shows the pedal height is at maximum $13$ cm. - This means the pedal is at the highest point relative to the horizontal. 5. **Equation of the function:** - The given function is $f(x) = 13 \sin(x - 270)$. - This represents a sine wave with amplitude $13$, phase shift $270^\circ$, and period $360^\circ$. - The phase shift moves the sine curve so that the maximum occurs at $x=0^\circ$. **Final answers:** - a) Period: $360^\circ$ (one full rotation), Amplitude: $13$ cm (radius of pedal path), Axis: $y=0$ cm (midline height). - b) Position at start ($x=0^\circ$): $13$ cm (maximum height). - c) Equation: $$f(x) = 13 \sin(x - 270)$$