Tim Gan Math
All Years

2012 TYS

Question 4

Question

In the triangle $ABC$, $AB=1$, angle $BAC=\theta $ radians and angle $ABC=\frac{3}{4}\pi $ radians (see diagram).

  1. Show that $AC=\frac{1}{\cos \theta -\sin \theta }$.

    [4]

  2. Given that $\theta $ is a sufficiently small angle, show that
    $AC\approx 1+a\,\theta +b\,{{\theta }^{2}}$,
    for constants $a$ and $b$ to be determined.

    [4]