waecmaths question:
Given that $\tan x=\tfrac{2}{3}$, where ${{0}^{\circ }}\le x\le {{90}^{\circ }}$, find the value of $2\sin x$
Option A:
$\frac{2\sqrt{13}}{13}$
Option B:
$\frac{3\sqrt{13}}{13}$
Option C:
$\frac{4\sqrt{13}}{13}$
Option D:
$\frac{6\sqrt{13}}{13}$
waecmaths solution:
$\begin{align} & \left| BC \right|=\sqrt{{{2}^{2}}+{{3}^{2}}} \\ & BC=\sqrt{13} \\ & \sin x=\frac{opp}{hyp}=\frac{2}{\sqrt{13}} \\ & 2\sin x=2\times \frac{2}{\sqrt{13}}=\frac{4}{\sqrt{13}}=\frac{4}{\sqrt{13}}\times \frac{\sqrt{13}}{\sqrt{13}}=\frac{4\sqrt{13}}{13} \\\end{align}$
maths year:
maths topics: