Given that $ \tan x = \frac{2}{3} $, where $0^\circ < x < 90^\circ$, Find the value of $2\sin x$.

Assessment: JAMB UTME - Mathematics - 2015 Subject: General Mathematics

Question 1 Report

\frac{2 \sqrt{13}}{13}

\frac{3 \sqrt{13}}{13}

\frac{4 \sqrt{13}}{13}

\frac{6 \sqrt{13}}{13}

Answer Details

tan x = $\frac{2}{3}$ (given), is illustrated in a right-angled $Δ$
thus m2 = 22 + 32
= 4 + 9 = 13
m = $\sqrt{13}$
Hence, 2sin x = 2 x $\frac{2}{m}$
2 x $\frac{2}{\sqrt{13}}$
= $\frac{4}{\sqrt{13}}$
= $\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}$
= $\frac{4 \sqrt{13}}{13}$

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Given that \( \tan x = \frac{2}{3} \), where \(0^\circ < x < 90^\circ\), Find the value of \(2\sin x\).

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Given that \( \tan x = \frac{2}{3} \), where \(0^\circ < x < 90^\circ\), Find the value of \(2\sin x\).

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