In the triangle $ABC$, $AB=1$, angle $BAC=\theta $ radians and angle $ABC=\frac{3}{4}\pi $ r

Question

In the triangle $ABC$, $AB=1$, angle $BAC=\theta $ radians and angle $ABC=\frac{3}{4}\pi $ radians (see diagram). Show that $AC=\frac{1}{\cos \theta -\sin \theta }$.[4] Given that $\theta$ is a sufficiently small angle, show that $AC\approx1+a\theta+b\theta^2$, for constants $a$ and $b$ to be determined.[4]

Accepted Answer

(i) $AC=\frac1{\cos\theta-\sin\theta}$; (ii) $a=1$, $b=\frac32$

N2012 P1 Q4

N2012 P1 Q4

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