<p>The following diagram represent a large Ferris wheel, with a diameter of 100 metres.</p>
<div class="graph-block" data-graph-config="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" data-width="300" data-height="200" style="width:300px;height:200px;max-width:100%;display:block;margin:0 auto;"></div>
<p>Let&nbsp;\(P\) be a point on the wheel. The wheel starts with \(P\) at the lowest point, at ground level. The wheel rotates at a constant rate, in an anticlockwise (counterclockwise) direction. One revolution takes \(20\) minutes.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down the height of \(P\) above ground level after</div><ol class="i-list"><li><div class="list-item-paragraph">\(10\) minutes;</div></li><li><div class="list-item-paragraph">\(15\) minutes.<span class="inline-marks">[2]</span></div></li></ol></li></ol>
<p>Let&nbsp;\(h(t)\) metres be the height of \(P\) above ground level after \(t\) minutes. Some values of \(h(t)\) are given in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 140px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p style="text-align: center;">\(t\)</p></th><th style="text-align: center; --cell-justify: center"><p style="text-align: center;">\(h(t)\)</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>\(0\)</p></td><td style="text-align: center; --cell-justify: center"><p>\(0.0\)<br></p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>\(1\)</p></td><td style="text-align: center; --cell-justify: center"><p>\(2.4\)</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>\(2\)</p></td><td style="text-align: center; --cell-justify: center"><p>\(9.5\)</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>\(3\)</p></td><td style="text-align: center; --cell-justify: center"><p>\(20.6\)<br></p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>\(4\)<br></p></td><td style="text-align: center; --cell-justify: center"><p>\(34.5\)<br></p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>\(5\)<br></p></td><td style="text-align: center; --cell-justify: center"><p>\(50.0\)<br></p></td></tr></tbody></table></div></div>
<ol class="abc-list" start="2"><li><ol class="i-list"><li><div class="list-item-paragraph">Show that&nbsp;\(h(8)=90.5\).</div></li><li><div class="list-item-paragraph">Find \(h(21)\).<span class="inline-marks">[4]</span></div></li></ol></li><li><div class="list-item-paragraph"><strong>Sketch</strong> the graph of \(h\), for&nbsp;\(0\leq t \leq 40\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Given that&nbsp;\(h\) can be expressed in the form \(h(t)=a\cos{bt}+c\), find \(a\), \(b\) and \(c\).<span class="inline-marks">[5]</span></div></li></ol>

The following diagram represent a large Ferris wheel, with a diameter of 100 metres.

Let \(P\) be a point on the wheel. The wheel starts with \(P\) at the lowest point, at ground level. The wheel rotates at a constant rate, in an anticlockwise (counterclockwise) direction. One revolution takes \(20\) minutes.

Write down the height of \(P\) above ground level after

Let \(h(t)\) metres be the height of \(P\) above ground level after \(t\) minutes. Some values of \(h(t)\) are given in the table below.

**Sketch** the graph of \(h\), for \(0\leq t \leq 40\).

Given that \(h\) can be expressed in the form \(h(t)=a\cos{bt}+c\), find \(a\), \(b\) and \(c\).

Trigonometric Equations and Identities

International Baccalaureate Standard Level Mathematics