<p>The diagram shows the graph of \(y = a \sin bx + c\), where&nbsp;\(b &gt; 0\), for&nbsp;\(-180^\circ \le x \le 180^\circ\). The graph has a maximum point at \(\left( 45^\circ, \frac{9}{2} \right)\) and a minimum point at \(\left( 135^\circ, -\frac{1}{2} \right)\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1770032512036-9yxw2mzu5h.png" style="max-width: min(320px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the amplitude, the period and the range of values of \(y\) corresponding to the interval. Hence find the values of \(a\), \(b\) and \(c\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Write down the coordinates of the other maximum point(s) and the other minimum point(s) of the graph in the given interval.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the range of the value of \(k\) for which the equation \(a \sin bx + c = k\) has four unique solutions for&nbsp;\(-180^\circ \le x \le 180^\circ\).</span></div></li></ol>

The diagram shows the graph of \(y = a \sin bx + c\), where \(b > 0\), for \(-180^\circ \le x \le 180^\circ\). The graph has a maximum point at \(\left( 45^\circ, \frac{9}{2} \right)\) and a minimum point at \(\left( 135^\circ, -\frac{1}{2} \right)\).

Find the amplitude, the period and the range of values of \(y\) corresponding to the interval. Hence find the values of \(a\), \(b\) and \(c\).

Write down the coordinates of the other maximum point(s) and the other minimum point(s) of the graph in the given interval.

Find the range of the value of \(k\) for which the equation \(a \sin bx + c = k\) has four unique solutions for \(-180^\circ \le x \le 180^\circ\).

Trigonometric Functions and Graphs

Question b331437a