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<p>In the triangle $ABC$, $AB=x$, $BC=y$, $AC=\frac{1}{6}$, angle $ABC=\frac{\pi }{6}$ radians and angle $ACB=\theta $ radians (see diagram).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-paragraph">Show that $\frac{x}{y}=\frac{2\sin \theta }{\cos \theta +\sqrt{3}\sin \theta }$.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">Given that $\theta $ is sufficiently small, express $\frac{x}{y}$ as a cubic polynomial in $\theta $.</div><p style="text-align: right;">[3]</p></li></ol></li><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-paragraph">Show that $\theta ={{\sin }^{-1}}\left( 3x \right)$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Find the Maclaurin series for $\theta $, up to and including the term in ${{x}^{3}}$.</div><p style="text-align: right;">[5]</p></li></ol></li></ol>

In the triangle $ABC$, $AB=x$, $BC=y$, $AC=\frac{1}{6}$, angle $ABC=\frac{\pi }{6}$ radians and angle $ACB=\theta $ radians (see diagram).

Maclaurin Series and Power Series - General

Maclaurin Series and Power Series

H2 Math

International Baccalaureate Higher Level Mathematics

2016 HCI P1 Q10

2016 HCI P1 Q10

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