<ol class="abc-list"><li><div class="list-item-paragraph">A hamster runs in its exercise wheel, rotating the wheel at a constant speed. The wheel has a diameter of 14 centimetres and the top of the wheel is positioned at a height of \(k\) centimetres above the floor of the cage.<br></div><div class="list-item-paragraph">A point at the top of the wheel is marked before the hamster starts to run, turning the wheel clockwise. The hamster takes 4 seconds to turn the wheel one complete revolution.</div><div class="list-item-paragraph">After \(t\) seconds, the height of the mark on the wheel above the floor of the cage is given by<br>\(h(t)=10+a\cos{\left(\frac{\pi}{2}t\right)}\) for&nbsp;\(0 \leq t \leq 150\)<br></div><div class="list-item-paragraph">After 26 seconds, the mark is 3 cm above the cage floor. Find \(k\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the value of \(a\).<span class="inline-marks">[3]</span></div></li></ol>

A hamster runs in its exercise wheel, rotating the wheel at a constant speed. The wheel has a diameter of 14 centimetres and the top of the wheel is positioned at a height of \(k\) centimetres above the floor of the cage.


A point at the top of the wheel is marked before the hamster starts to run, turning the wheel clockwise. The hamster takes 4 seconds to turn the wheel one complete revolution.

After \(t\) seconds, the height of the mark on the wheel above the floor of the cage is given by
\(h(t)=10+a\cos{\left(\frac{\pi}{2}t\right)}\) for \(0 \leq t \leq 150\)


After 26 seconds, the mark is 3 cm above the cage floor. Find \(k\).

Trigonometric Functions and Graphs

International Baccalaureate Standard Level Mathematics