<p>It is given that&nbsp;\(\mathrm{f}(x) = 2\sin\frac{x}{2}\) and \(\mathrm{g}(x) = 3\cos x + 1\), where&nbsp;\(0 \le x \le 2\pi\).</p>
<ol class="abc-list"><li data-list-item-id="imported-item-block-1-item-0" data-list-item-path="imported-item-block-1-item-0"><div class="list-item-paragraph">State the period of \(\mathrm{f}(x)\).<span class="inline-marks">[1]</span></div></li><li data-list-item-id="imported-item-block-1-item-1" data-list-item-path="imported-item-block-1-item-1"><div class="list-item-paragraph">State the smallest value of \(\mathrm{f}(x)\).<span class="inline-marks">[1]</span></div></li><li data-list-item-id="imported-item-block-1-item-2" data-list-item-path="imported-item-block-1-item-2"><div class="list-item-paragraph">State the largest value of \(\mathrm{g}(x)\).<span class="inline-marks">[1]</span></div></li><li data-list-item-id="imported-item-block-1-item-3" data-list-item-path="imported-item-block-1-item-3"><div class="list-item-paragraph"><p>Sketch on the same axes, the graphs of \(y = \mathrm{f}(x)\) and \(y = \mathrm{g}(x)\) for&nbsp;\(0 \le x \le 2\pi\).</p><p>Label your graphs clearly.</p><span class="inline-marks">[4]</span></div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1788533193507-uobv0qm1g3a.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODg1MzMxOTM1MDctdW9idjBxbTFnM2EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4ODU0OTQwNSwiZXhwIjoxNzg4NTQ5NzA1fQ.0vzld_anlEjWCBQSgfQOC1QB_QTicxQ6ULxSyJW9j40" alt="List item image" class="aligncenter custom-width" style="max-width: min(600px, 100%); height: auto;" /></div></li><li data-list-item-id="imported-item-block-1-item-4" data-list-item-path="imported-item-block-1-item-4"><div class="list-item-paragraph"><p>The solutions to the equation \(\mathrm{f}(x) = \mathrm{g}(x)\) for \(0 \le x \le 2\pi\) are \(a\) and \(b\), where \(a &lt; b\).</p><p>State, in terms of \(a\) and \(b\), the range of values of \(x\) for which \(\mathrm{f}(x) &gt; \mathrm{g}(x)\).</p><span class="inline-marks">[1]</span></div></li></ol>

It is given that \(\mathrm{f}(x) = 2\sin\frac{x}{2}\) and \(\mathrm{g}(x) = 3\cos x + 1\), where \(0 \le x \le 2\pi\).

State the smallest value of \(\mathrm{f}(x)\).

State the largest value of \(\mathrm{g}(x)\).

<p>Sketch on the same axes, the graphs of \(y = \mathrm{f}(x)\) and \(y = \mathrm{g}(x)\) for&nbsp;\(0 \le x \le 2\pi\).</p><p>Label your graphs clearly.</p>

<p>The solutions to the equation \(\mathrm{f}(x) = \mathrm{g}(x)\) for \(0 \le x \le 2\pi\) are \(a\) and \(b\), where \(a &lt; b\).</p><p>State, in terms of \(a\) and \(b\), the range of values of \(x\) for which \(\mathrm{f}(x) &gt; \mathrm{g}(x)\).</p>